  We consider vector valued weak solutions $u:\Omega_T\to \mathbb{R}^N$ with
$N\in \mathbb{N}$ of degenerate or singular parabolic systems of type
\begin{equation*}
  \partial_t u - \mathrm{div} \, a(z,u,Du) = 0 \qquad\text{in}\qquad \Omega_T=
\Omega\times (0,T), \end{equation*} where $\Omega$ denotes an open set in
$\mathbb{R}^{n}$ for $n\geq 1$ and $T>0$ a finite time. Assuming that the
vector field $a$ is not of Uhlenbeck-type structure, satisfies $p$-growth
assumptions and $(z,u)\mapsto a(z,u,\xi)$ is H\"older continuous for every
$\xi\in \mathbb{R}^{Nn}$, we show that the gradient $Du$ is partially H\"older
continuous, provided the vector field degenerates like that of the
$p$-Laplacian for small gradients.
