Gray codes, where two consecutive codewords differ in exactly one position by plusmn1, are given. In a single-radix code, all dimensions have the same base, say, kappa, whereas, in a mixed-radix code, the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed-radix Gray codes are presented. It is shown how these codes can be used as a basis for constructing edge-disjoint Hamiltonian cycles in mixed-radix toroidal networks when the number of dimensions n = 2r for some r ges 0. Efficient algorithms for the generation of these codes are then shown.