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Let $a,b,n$ be three positive integers such that $a\equiv b\pmod 2$ and$n\geq b(a+b)(a+b+2)/(2a)$. Let $G$ be a graph of order $n$ with minimum degreeat least $a+b/a-1$. We show that $G$ has an $(a,b)$-parity factor, if$max\{d_G(u),d_G(v)\}\geq \frac{an}{a+b}$ for any two nonadjacent vertices$u,v$ of $G$. It is an extension of Nishimura's results for the existence of$k$-factors (\emph{J. Graph Theory}, \textbf{16} (1992), 141--151) andgeneralizes Li and Cai's result in some senses (\emph{J. Graph Theory},\textbf{27} (1998), 1--6). These conditions are tight.

A Degree Condition for a Graph to have $(a,b)$-Parity Factors