The Priifer transformation has been generalized to selfadjoint matrix differential equations by J. Barrett and others. Those results are extended to nonselfadjoint abstract systems of the form considered by Kamke in the scalar case and Reid in the matrix case. Generalizations of the Prufer transformation [1] to selfadjoint matrix differential systems of the form (1) Y'f = B(x)Z; Z' = D(x) Y (a < x < oo) have been studied by Barrett [2], Etgen [3], [4], and Reid [5], [6]. Hille [7] and Benson and the author [8] have established Priifer transformations for abstract differential systems of the form (1) where B(x), D(x), Y(x) and Z(x) take their values in a Banach algebra $. In all these studies the selfadjointness conditions B(x) _ B*(x); D(x) =_ D*(x) play an essential role. The purpose of this note is to establish a Priifer transformation for nonselfadjoint $i-valued matrix differential systems of the form (2) y= A(x)Y + B(x)Z, Z' = -D(x)Y + E(x)Z. Such a transformation has been established in the scalar case by Kamke [9], [10], and (by different techniques) in the matrix case by Reid [6]. It is assumed that A(x), B(x), D(x), and E(x) are strongly continuous M3-valued functions on the semi-infinite interval I = [a, so), and all derivatives below are to be taken in the strong topology. In passing from (1) to the more general system (2), we lose the relation (Y*Z Z* Y)' 0_ which is used in constructing prepared or solutions in the selfadjoint case. As pointed out to the author by W. T. Reid, the condition that a solution of (1) be conjoined is analogous to restricting oneself to real solutions in the scalar case. Accordingly our Priifer transformation for (2) is motivated by a study by Barrett [11] of a Priifer transformation for complex valued solutions of a scalar system of the form (1). Received by the editors January 4, 1971. AMS 1969 subject classifications. Primary 3495; Secondary 3442.