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are known provided the characteristic values of the matrix a = (aif) have nonzero real parts; cf., for example, [l]. Here the r¿ are uniformly a.p. in t for (x,-, • • • , x„) in some region of Euclidean «-space. Amerio [3] has obtained such conditions for somewhat more specialized systems where some characteristic values of A may be pure imaginary; however, all must be distinct from zero. In case w = 2, sufficient conditions for the existence, uniqueness, and asymptotic stability of a.p. solutions are known even if one of the characteristic values of A is zero. In fact, the system considered in [2] is

Almost periodic solutions for systems of differential equations near points of nonlinear first approximation