  We consider multidimensional differential systems (total differential systems
and partial differential systems) with R-differentiable coefficients. We
investigate the problem of the existence of R-holomorphic solutions,
R-differentiable integrals, and last multipliers. The theorem of existence and
uniqueness of R-holomorphic solution is proved. The necessary conditions and
criteria for the existence of R-differentiable first integrals, partial
integrals, and last multipliers are given. For a completely solvable total
differential equation with R-holomorphic right hand side are constructed the
classification of R-singular points of solutions and proved sufficient
conditions that equation have no movable nonalgebraical R-singular points. The
spectral method for building R-differentiable first integrals for linear
homogeneous first-order partial differential systems with R-linear coefficients
is developed.
