  The main purpose of this paper is to study multi-parameter singular integral
operators which commute with Zygmund dilations. We introduce a class of
singular integral operators associated with Zygmund dilations and show the
boundedness for these operators on $L^p, 1<p<\infty$, which covers those
studied by Ricci--Stein \cite{RS} and Nagel--Wainger \cite{NW}
