SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


                                    FORM 6-K


                        Report of Foreign Private Issuer


                        Pursuant to Rule 13a-16 or 15d-16
                     of the Securities Exchange Act of 1934


                           For the month of June, 2004

                              RYANAIR HOLDINGS PLC
                 (Translation of registrant's name into English)

                      c/o Ryanair Ltd Corporate Head Office
                                 Dublin Airport
                              County Dublin Ireland
                    (Address of principal executive offices)


Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F.

                         Form 20-F..X.. Form 40-F.....


Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange
Act of 1934.

                               Yes ..... No ..X..


If "Yes" is marked, indicate below the file number assigned to the registrant
in connection with Rule 12g3-2(b): 82- ________


               RYANAIR'S CUSTOMER SERVICE STATISTICS FOR MAY 2004.

Ryanair, Europe's No.1 low fares airline, today (Friday, 4th June 2004) released
its customer service statistics for May 2004. Ryanair is committed to publishing
customer  service  statistics  each month and these confirm that Ryanair is also
No. 1 for Customer Service.

     -    93.2% of all Ryanair's  15,750 flights during the month of May arrived
          on time.

     -    Ryanair  has set the  standard  as the No.1  on-time  airline  beating
          Easyjet  every  week in 2003  and  continues  into  2004 as the No.  1
          airline for the fewest cancellations.

     -    Complaints   registered  at  less  than  1(0.48)  complaint  per  1000
          passengers.

     -    Mislaid  baggage  registered at less than 1(0.64) mislaid bag per 1000
          passengers.




       CUSTOMER SERVICE STATISTICS- MAY 2004                  2003      2004
                                                                   
     On-time flights*                                          91%       93%
     Complaints per 1 000 pax                                 0.76      0.48
     Baggage complaints per 1 000 pax                         0.64      0.64
     Complaints answered with 7 days                          100%      100%

     *Verified by the CAA 3 months in arrears



Ends:                            Friday, 4th June 2004

For further information:

Paul Fitzsimmons - Ryanair     Pauline McAlester - Murray Consultants
Tel: 00 353 1 812 1228         Tel: 00 353 1 4980 300



Ryanair Monthly  Statistics - Compared with Association of European Airlines The
following are based on the Association of European Airlines monthly  performance
statistics  for our  major  competitors  for the  month of  April  2004 and also
figures published on other airline




Ryanair No. 1 on time major airline in Europe

Airline                                        Ranking               %
                                                              
Ryanair                                              1            94.3
SAS                                                  2            91.2
Lufthansa                                            3            88.5
Easyjet                                              4            88.0
Air France                                           5            84.1
British Airways                                      5            84.1
Alitalia                                             6            82.7

             % Flights arriving within 15 minutes of scheduled time






Major airlines for fewest lost bags*

Airline           Ranking       Baggage Lost Per 1000 Passengers
                                                       
Ryanair                 1                                  0.83
SAS                     2                                  10.1
Alitalia                3                                  13.7
Air France              4                                  14.1
British Airways         5                                  14.0
Lufthansa               6                                  13.6
Austrian                7                                  15.5
EasyJet                            Refuse to Publish






Major airline for fewest cancellations*

Airline                     Ranking                % flights completed
                                                             
Ryanair                          1                                99.8
Lufthansa                        2                                99.6
Austrian                         3                                99.5
British Airways                  4                                99.4
SAS                              5                                99.1
Alitalia                         6                                98.6
Air France                       7                                97.3
Easyjet                                   Refuse to Publish

*Source:Ryanair monthly statistics compared to Association of European Airlines
-April 04. Punctuality statisticsverified by the CAA 3 months in arrears.






Ryanair/Easyjet Punctuality Comparisons

     Week Ending       Ryanair        easyJet          Ryanair Position
                                                        
     1    04-Jan           90%            73%                         1
     2    12-Jan           91%            80%                         1
     3    19-Jan           95%            84%                         1
     4    26-Jan           95%            89%                         1
     5    01-Feb           85%            64%                         1
     6    08-Feb           93%            81%                         1
     7    15-Feb           95%            84%                         1
     8    22-Feb           91%            84%                         1
     9    29-Feb           89%            69%                         1
    10    07-Mar           93%            80%                         1
    11    14-Mar           93%            80%                         1
    12    21-Mar           92%            82%                         1
    13    28-Mar           95%            88%                         1
    14    04-Apr           94%            87%                         1
    15    11-Apr           93%            88%                         1
    16    18-Apr           95%            85%                         1
    17    25-Apr           96%            92%                         1
    18     2-May           94%            85%                         1
    19     9-May           93%            81%                         1
    20    16-May           95%            84%                         1
    21    23-May           94%            87%                         1

                   Source:www.ryanair.com and Easyjet website



                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, hereunto duly authorized.

                                    RYANAIR HOLDINGS PLC


Date:  4 June 2004

                                    By:___/s/ Howard Millar____

                                    H Millar
                                    Company Secretary & Finance Director