We give a proof of the Hölder continuity of weak solutions for the doubly nonlinear parabolic equation in the degenerate case. The analysis discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods. The focus of the talk will be on the precise construction of the sequence of nested and shrinking cylinders where the oscillation of the solution is to be evaluated, and its relation to the structure of the pde. This is a joint work with Tuomo Kuusi and Juhana Siljander (Aalto University, Finland) that will soon appear in Indiana Univ. Math. J.