In this paper we are concerned with the Hölder estimates of solutions of the Cauchy problem for the degenerate parabolic Eq. (1) with the initial data (2), where the diffusion function G ( u ) can be a constant on a non-zero measure set, such as the equations of two-phase Stefan's type. Under the condition | GG "/ G ' 2 | h g , g 2 h 1/2 N , the global estimates | o ( G f ( u ))| h M , on R N ‐ R + , is obtained by using the maximum principle, where f is a constant given in (9).