Abstract: In this paper, by thinking of the complex analysis in several variables, first we prove the two Poincare-Bertrand transformation formulae of the singular repeated integrals on char-acteristic manifold in Clifford analysis,and then proceed to consider the Fredholm's theory for singular integral equations, and give the regularization opelator of the singular integral equations.

Key words: Singular integral, Characteristic manifold, Clifford analysis