  The work is devoted to investigation of the canonical structure of regular,
in domain of definition ${\cal U}\subseteq {\mathbb R}^{m}$, the pencil of
matrix-functions $A(x)+\lambda B(x)$. It is supposed that $\det A(x)\equiv 0$
and $\det B(x)\equiv 0\;\; \forall \ x \in {\cal U}$, and all roots of the
characteristic equation $\det(A(x)+\lambda B(x))=0$ with $\lambda=\lambda
(x)\in C^{p}({\cal U})$, are of constant multiplicity.
