The author presents some regularity results concerning local minimizers of variational integrals with nonautonomous integrands like \[ \int _{\Omega }\left \{ F\left (\cdot ,\varepsilon (w)\right) -f\cdot w\right \} dx \; \text{ in the class } \left \{ w\in W_{\mathrm{loc}}^{1,p}\left (\Omega ,\mathbb {R}^{n}\right) :\operatorname {div}w=0\right \}. \] A \(\left (p,q\right) \)-elliptic growth condition for the potential \(F\left (x,\varepsilon \right) =g\left (x,\left | \varepsilon \right | \right) \) is assumed. The author proves, under some assumptions, that for a local minimizer \(u:\mathbb {R}^{n}\supset \Omega \rightarrow \mathbb {R}^{n}\) there is an open subset \(\Omega _{0}\) (\(\Omega _{0}=\Omega \) for \(n=2\)) with full Lebesgue-measure such that \(u\) belongs to the space \(C^{1,\alpha }\left (\Omega _{0},\mathbb {R}^{n}\right) \) for any \(\alpha \in \left (0,1\right)\). The result may be applied to weak solutions of the nonlinear Stokes type system \(\operatorname {div} \left \{ \nabla F\left (\varepsilon \left (v\right) \right) \right \} =\nabla \pi -f\) in \(\Omega \).