CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


Name of Issuer: VANGUARD EXPLORER FUND

     In connection with the Report on Form N-CSR of the above-named  issuer that
is accompanied by this certification,  the undersigned hereby certifies,  to his
knowledge, that:

1.   The Report fully complies with the  requirements  of Section 13(a) or 15(d)
     of the Securities Exchange Act of 1934; and

2.   The information  contained in the Report fairly  presents,  in all material
     respects, the financial condition and results of operations of the issuer.


Date:  December 12, 2003
                                                        /S/ JOHN J. BRENNAN
                                                   -----------------------------
                                                                 John J. Brennan
                                                         Chief Executive Officer










                CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


Name of Issuer:  VANGUARD EXPLORER FUND

     In connection with the Report on Form N-CSR of the above-named  issuer that
is accompanied by this certification,  the undersigned hereby certifies,  to his
knowledge, that:

1.   The Report fully complies with the  requirements  of Section 13(a) or 15(d)
     of the Securities Exchange Act of 1934; and

2.   The information  contained in the Report fairly  presents,  in all material
     respects, the financial condition and results of operations of the issuer.


Date:  December 12, 2003
                                                        /S/ THOMAS J. HIGGINS
                                                    ----------------------------
                                                               Thomas J. Higgins
                                                                       Treasurer