This paper presents a uniform semiglobal exponential stability (USGES) proof for a class of proportional line-of-sight (LOS) guidance laws used for vehicle path-following control. The LOS guidance law under consideration is a lookahead-based guidance law for marine craft. The USGES proof extends previous results that only guarantee global K-exponential stability. Typical applications are marine craft and aircraft motion control systems for path following where the total system is a cascade of the motion controller and guidance law error dynamics. (C) 2014 Elsevier Ltd. All rights reserved.