  We consider Stokes system in bounded domains and we present conditions of
given data, in particular, boundary data, which ensure H\"older continuity of
solutions. For H\"older continuous solutions for the Stokes system the normal
component of boundary data requires a bit more regular than boundary data of
H\"older continuous solutions for the heat equation. We also construct an
example, which shows that H\"older continuity is no longer valid, unless the
proposed condition of boundary data is fulfilled. As an application, we
consider a certain general types of nonlinear systems coupled to fluid
equations and local well-posedness is established in H\"older spaces.
