  Let $(R,\mathfrak{m})$ be a quasi-unmixed local ring and $I$ an equimultiple
ideal of $R$ of analytic spread $s$. In this paper, we introduce the
equimultiple coefficient ideals. Fix $k\in \{1,...,s\}.$ The largest ideal $L$
containing $I$ such that $e_{i}(I_{\mathfrak{p}})=e_{i}(L_{\mathfrak{p}})$ for
each $i \in \{1,...,k\}$ and each minimal prime $\mathfrak{p}$ of $I$ is called
the $k$-th equimultiple coefficient ideal denoted by $I_{k}$. It is a
generalization of the coefficient ideals firstly introduced by Shah \cite{S}
for the case of $\mathfrak{m}$-primary ideals. We also see applications of
these ideals. For instance, we show that the associated graded ring $G_{I}(R)$
satisfies the $S_{1}$ condition if and only if $I^{n}=(I^{n})_{1}$ for all $n$.
