One of the main results in a recent paper [P.H.A. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208-1213] is extended to a more general nonlinear differential system with time-varying delays. A restrictive condition for global exponential stability in the above paper is also removed. (C) 2012 Elsevier Ltd. All rights reserved.