The spin‐wave instability theory of nonlinear effects in ferromagnetic insulators developed by Suhl for perpendicular pumping and by Schlo¨mann for parallel pumping has been extended to include pumping with an arbitrary microwave field configuration. The theory is applicable to samples of ellipsoidal shape, magnetized to saturation along one principal axis, but not necessarily an axis of rotational symmetry as in the Suhl theory. The theory, in its present form, is quite versatile and applicable to a large variety of situations which are not accessible on the basis of the earlier calculations. Equations are developed specifically for first‐order processes. Several examples are considered to demonstrate the versatility of the theory: (1) Perpendicular pumping with a linearly polarized microwave field; (2) oblique pumping with a linearly polarized field at an angle between 0° and 90° to the static field; (3) perpendicular pumping with a circularly polarized field rotating in the anti‐Larmor sense.