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We study solutions ${\bf v}$ of the parabolic system of PDE $$\partial_t\left(D\psi({\bf v})\right)=\text{div}DF(D{\bf v}). $$ Here $\psi$and $F$ are convex functions, and this is a model equation for more generaldoubly nonlinear evolutions that arise in the study of phase transitions inmaterials. We show that if ${\bf v}$ is a weak solution, then $D{\bf v}$ islocally H\"older continuous except for possibly on a lower dimensional subsetof the domain of ${\bf v}$. Our proof is based on compactness properties ofsolutions, two integral identities and a fractional time derivative estimatefor $D{\bf v}$.

Partial regularity for doubly nonlinear parabolic systems of the first type