  In mesoscopic two-gap superconductors with sizes of the order of the
coherence length noncomposite vortices are found to be thermodynamically stable
in a large domain of the $T - H$ phase diagram. In these phases the vortex
cores of one condensate are spatially separated from the other condensate ones,
and their respective distributions can adopt distinct symmetries. The
appearance of these vortex phases is caused by a non-negligible effect of the
boundary of the sample on the superconducting order parameter and represents
therefore a genuine mesoscopic effect. For low values of interband Josephson
coupling vortex patterns with $L_1 \neq L_2$ can arise in addition to the
phases with $L_1 =L_2$, where $L_1$ and $L_2$ are total vorticities in the two
condensates. The calculations show that noncomposite vortices could be observed
in thin mesoscopic samples of MgB$_{2}$.
