Observations of the A5p star KIC 8677585 obtained during the Kepler 10-d commissioning run with 1-min time resolution show that it is a rapidly oscillating Ap (roAp) star with several frequencies with periods near 10 min. In addition, a low frequency at 3.142 d−1 is also clearly present. Multiperiodic γ Doradus (γ Dor) and δ Scuti (δ Sct) pulsations, never before seen in any Ap star, are present in Kepler observations of at least three other Ap stars. Since γ Dor pulsations are seen in Ap stars, it is likely that the low frequency in KIC 8677585 is also a γ Dor pulsation. The simultaneous presence of both γ Dor and roAp pulsations and the unexpected detection of δ Sct and γ Dor pulsations in Ap stars present new opportunities and challenges for the interpretation of these stars. Since it is easy to confuse Am and Ap stars at classification dispersions, the nature of these Ap stars in the Kepler field needs to be confirmed.