A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitary angle &psgr; with respect to the earth's magnetic field B0. In particular, we examine the phase trapping (PT) mechanism believed by some to be responsible for the generation of VLF emissions. The phase considered in this study is the phase &ggr; between the right-hand circularly polarized component of the wave magnetic field perpendicular to B0 and the component of the energetic particle velocity vector perpendicular to B0. This model is an extension of one developed in earlier work [Bell, 1965; Dysthe, 1971; Nunn, 1974> involving the special case where &psgr;=0. The extended theory predicts that for any finite value of &psgr; there is a range of resonant particle pitch angle &agr; for which &ggr; is not bounded within the range 0≲‖&ggr;‖37¿. For interactions far from the magnetic equator, &psgr; variations appear to be less important than gradients in B0 and in this case we calculate the wave power increase necessary to produce the same PT efficiency for typical nonducted waves as that appropriate to ducted waves. The component of the wave electric field parallel to B0 generally enhances the strength of the PT process and tends to dominate the process for moderate to high &psgr; at midfrequency. It is consluded that near the magnetic equatorial plane gradients of &psgr; may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.