We develop a method for calculating the Lyapunov characteristic exponents of lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with lattice size is found. In Ref.1, we have studied chaos in lattice gauge systems by obtaining the largest Lyapunov exponents. The method used there, though straightf...