The influence of external field on thin ferromagnetic films with spin-reorientation transitions (SRTs) is explored in the presence of different orders of thickness-dependent uniaxial anisotropy. The two principal configurations are addressed and the first two anisotropy contributions are examined. A simple and natural representation of the field-induced SRTs has been found. It preserved the linearity of the thickness-driven trajectories even with field. The crosspoints of these trajectories with the phase borderlines correspond to crossover thicknesses of a linear type for positive second-order anisotropy contributions and of both linear and nonlinear types for negative second-order anisotropies. In the latter case, the nonlinear boundaries correlate with the coexistance of phases which brings about first-order-like reorienations and concommittant hysteresis effects. Practical schemes are proposed for the determination of the complete set of anisotropy parameters from measured field dependences of the crossover thicknesses.