Abstract: This article studies the inhomogeneous Moisil-Theodorsco system in the space R³, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R³, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.

Key words: Moisil-Theodorsco System, Operator T, Holder continuous, Riemann-Hilbert boundary value problem