Low-frequency modulations of the fluxes of magnetospheric charged particles are often observed in conjunction with geomagnetic pulsations. In some cases, the flux modulations depend on detector look direction even after effects arising from pitch angle anisotropy have been removed. For a detector on a spinning spacecraft, the look direction dependence creates flux modulations ordered by the spin phase angle, so the term 'spin phase dependence' provides a convenient description of the phenomenon considered in this paper. Spin phase dependence occurs only when the gyroradius of the detected particles (charge q; energy, W) is comparable with some other characteristic length of the problem. In particular, spin phase dependence occurs when the particle gyroradius aL is comparable with &lgr;⊥, the wavelength transverse to B. ATS 6 and GEOS have provided examples of this type of 'finite gyroradius' effect. Wave-related spin phase dependence may also arise with aL≪&lgr;⊥. For example, a wave convecting a steep spatial gradient in the particle density n(W) back and forth creates spin phase dependent flux oscillations if aL≂n(W)/‖∇n(W)‖. This situation is described and related to ISEE boundary wave studies. Gyration acceleration, i.e., acceleration by the wave electric field E, leads to spin phase dependence of the flux of particles for which aL≂W/&ggr;qE, where &ggr; is the power law coefficient of the differential particle flux, again without any restriction to short wavelengths. Some OGO 5 and ISEE wave analyses have relied on this type of spin phase dependence. Gyration acceleration has also been invoked to explain particle pulsations seen on the nonspinning ATS 6 spacecraft, albeit in circumstances where the spin dependence cannot be checked. Finally, spin phase dependences may be produced by large-scale standing wave structure parallel to the ambient magnetic field, an effect which appers in some ISEE particle data.