The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T > 0 in one- or two-dimensional Heisenberg and XY systems with long−range interactions decreasing as R⁻α with a sufficiently large exponent α. For oscillatory interactions, ferromagnetic long-range ordert T > 0 is ruled out if α ≥ 1 (D = 1) or α > 5/2(D = 2). For systems with monotonically decreasing interactions, ferro- or antiferromagnetic long-range order at T > 0 is ruled out if α ≥ 2D.