  We prove higher integrability of the spatial gradient of weak solutions to
parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general
Orlicz function. The parabolic systems need be neither degenerate nor singular.
Our result is a generalized version of the one of J. Kinnunen and J. Lewis
[Duke Math. J. 102 (2000), no. 2, 253--271] for the parabolic $p$-Laplace
systems.
