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 not equal 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 MgB2.