We study the homogenization problem for matrix strongly elliptic operators on L-2(R-d)(n) of the form A(epsilon) = - div A(x , x/epsilon)del. The function A is Lipschitz in the first variable and periodic in the second. We do not require that A* = A, so A(epsilon) need not be self-adjoint. In this paper we provide the first two terms of a uniform approximation for (A(epsilon) - mu)(-1) and the first term of a uniform approximation for del(A(epsilon) - mu)(-1) as epsilon -> 0. Primary attention is paid to proving sharp-order bounds on the errors of approximation. (C) 2021 Elsevier Inc. All rights reserved.