  We consider a pencil of matrix Sturm-Liouville operators on a finite
interval. We study properties of its spectral characteristics and inverse
problems that consist in recovering of the pencil by the spectral data:
eigenvalues and so--called weight matrices. This inverse problem is reduced to
a linear equation in a Banach space by the method of spectral mappings.
Constructive algorithm for the solution of the inverse problem is provided.
