Let [Formula: see text] and [Formula: see text] be entire matrix-valued functions of a complex argument [Formula: see text] (entire matrix pencils) and [Formula: see text]. Let [Formula: see text] and [Formula: see text] denote the numbers of the characteristic values of [Formula: see text] taken with their multiplicities located inside and outside [Formula: see text], respectively. Besides [Formula: see text] can be infinite. We consider the following problem: how “close” should be [Formula: see text] and [Formula: see text] in order to provide the equalities [Formula: see text] and [Formula: see text]? We restrict ourselves by the entire pencils of order not more than two. Our results are new even for polynomial pencils.