  We consider holomorphic deformations of Fuchsian systems parameterized by the
pole loci. It is well known that, in the case when the residue matrices are
non-resonant, such a deformation is isomonodromic if and only if the residue
matrices satisfy the Schlesinger system with respect to the parameter. Without
the non-resonance condition this result fails: there exist non-Schlesinger
isomonodromic deformations. In the present article we introduce the class of
the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal
deformation is also an isomonodromic one. In general, the class of the
isomonodromic deformations is much richer than the class of the isoprincipal
deformations, but in the non-resonant case these classes coincide. We prove
that a deformation is isoprincipal if and only if the residue matrices satisfy
the Schlesinger system. This theorem holds in the general case, without any
assumptions on the spectra of the residue matrices of the deformation. An
explicit example illustrating isomonodromic deformations, which are neither
isoprincipal nor meromorphic with respect to the parameter, is also given.
