Using the one sided singular integrals with singularities of high order,the properties of Cauchy type integrals with kernel density of class H  near the ends are generalized to those with that of class H  n .

Then using integration by parts and stokes formula,the authors give the definition of Hadamard principal value of the higher order singular integral (t) whose singularities are of orders 2n.

Abstract By using the Hadamard s idea for principal value of high order singular inte-grals, we study induction definition, existence of Hadamard principal value, recurrence formula,computational and differential method, Poincare-Bertrand permutation formula, and Holdercontinuity for six kind quasi Bochner-Martinelli type high order singular integrals in real Clif-ford analysis.

In the first part of this paper, by the think of Hadamard principal value andthe think of induction, in view of prove the six lemma, we consider induce define, existence ofHadamard principal value, recurrence formula, compute formula and twelve differefltial formulafor three kind high order singular integrals in real Clifford analysis.

According to the idea of Hadamard principle value for high order singular integral and the idea of induction, the authors discuss the existence of Hadamard principle value, recursive formula, computation formula and differential formula on the sense of Hadamard principle value for Quasi-Bochner-Martinelli-type high order singular integral in real Clifford analysis.