中文摘要：

首先利用StokeS-Green定理得到了复k-超正则函数的必要条件.其次得到了复k-超正则函数和复k-超调和函数的充要条件.最后讨论了复k-超正则函数和复k-超调和函数的关系：已知一个复k-超调和函数u（z）,局部存在复k-超正则函数f（z）使得Pf（z）=u（z）等.

英文摘要：

A necessary condition of complex k-hypermonogenic functions is obtained by virtue of Stokes-Green theorem at first.Next some equivalent conditions of complex k-hypermonogenic functions and of complex k-hyperharmonic functions are given.Finally,the relationships between complex k-hypermonogenic functions and complex k-hyperharmonic functions are discussed：for a given complex k-hyperharmonic function u（z） there exists locally a complex k-hypermonogenic function f（z） such that Pf（z） = u{z）,and so on.