Introduction.-Let C denote the space of continuous functions from [-h, 01 into Rm, m-dimensional Euclidean spa.ce, h > 0, with the norm in C given by 111 = max 1{(u) l, -h s, by x,(u) = x(t + u), -h s u s 0. With this notation (due to Hale4) and the above definitions, we may write the linear functional differential equation with periodic coefficients as follows: