An approximate normal mode analysis of plasma current diffusion in tokamaks is presented. The work is based on numerical solutions of the current diffusion equation in cylindrical geometry. Eigenvalues and eigenfunctions are shown for a broad range of plasma conductivity profile shapes. Three classes of solutions are considered that correspond to three types of tokamak operation. Convenient approximations to the three lowest eigenvalues in each class are presented, and simple formulas for the current relaxation time scales are given and applied to several cases of simple current relaxation as well as noninductive current drive. Simulations of current relaxation with and without current redistribution caused by a ‘‘sawtooth’’ model show that sawteeth can considerably shorten the relaxation time if the sawtooth region extends tor∼a/2.