An L-1 type small-gain stability analysis approach is developed in this paper on linear systems subject to time-varying delays, which reinforces the existing H-infinity small-gain stability conditions for the same type of systems. A distinctive feature of this approach is that it requires no knowledge of delay variation rate and hence is more broadly applicable when this information is unavailable. While because of this generality the stability conditions may suffer from their conservatism, we show that there are important instances where the conditions are in fact nonconservative, and may fare better than those developed elsewhere for fast varying delays. (C) 2014 Elsevier Ltd. All rights reserved.