Gyromotion is studied by applying averaging techniques to exact equations for the guiding‐center position, magnetic moment, and gyrophase. A static nonuniform forceFis shown to shift the gyrofrequency from &OHgr; to &ohgr;=&OHgr;−∇⊥⋅(F/2m&OHgr;). The effects of this gyrofrequency shift on heating are discussed, as is the prospect of experimentally observing the phenomenon. It is also shown that an oscillatory force of sufficient amplitude, whose frequency &ohgr;* is close to &OHgr;, can cause phase locking, i.e., can force the particle to gyrate at the driving frequency &ohgr;*. A rough criterion for an electrostatic wave with electric fieldEto cause phase locking is thatvE/&rgr;&dgr;&ohgr;≥1, wherevE=cE/B, &rgr; is the gyroradius, and &dgr;&ohgr;=&ohgr;*−&OHgr;. Thus a weak wave can cause phase locking if the frequency mismatch is small. Phase locking is enhanced if the magnetic field has a well, which provides a large volume over which ‖B‖ is nearly uniform. Comparison with experimental measurements on the 2XIIB magnetic mirror experiment [J. Phys., Coll. 6, Suppl. No. 12, 38, C6 (1977)] shows that phase locking may account for the puzzling observation of a highly monochromatic wave at the central cyclotron frequency.