This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations u t = Δ G(u) + ∑ N j=1 f j (u) x j + h(u), with the initial data u(x, 0) = u 0 (x 1 , x 2 ,..., x N ), where the diffusion function G(u) can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function G(u) with respect to the space variables are obtained by using the maximum principle.