A study is made of the penetration of a-c flux into magnetic materials with a B-H relation which possesses saturation, but not hysteresis. Maxwell's nonlinear equations are derived for the case where directions of B-H coincide and remain constant except for complete reversal, and H is assumed to vary between equal and opposite limits. Penetration of such fields into semi-infinite solids and into plates of finite thickness is considered, and proper boundary conditions are derived. Solution of the linear, constant-permeability case is reviewed, and various methods of integrating the nonlinear Maxwell equations are presented. Solutions, based on approximate, numerical, finite-difference methods have been programmed on high-speed computing machines, and carried through successfully.