  In this paper we examine on a pair of adjoint functors $(\phi
^{\ast},\phi_{\ast})$ for a subcategory of the category of crossed modules over
commutative algebras where $\phi ^{\ast}:\mathbf{XMod}$\textbf{/}$%
Q\rightarrow $ $\mathbf{XMod/}P$, pullback, which enables us to move from
crossed $Q$-modules to crossed $P$-modules by an algebra morphism $\phi
:P\rightarrow Q$ and $\phi_{\ast}:\mathbf{XMod}$\textbf{/}$P\rightarrow $
$\mathbf{XMod/}Q$, induced. We note that this adjoint functor pair $(\phi
^{\ast},\phi_{\ast})$ makes $p:\mathbf{XMod}\rightarrow $ $k$\textbf{-Alg}into
a bifibred category over $k$\textbf{-Alg}, the category of commutative
algebras, where $p$ is given by $p(C,R,\partial)=R.$
  Also, some examples and results on induced crossed modules are given.
