A particularly convenient method for the calculation of approximate traveltimes in a two‐dimensional (2-D( medium has become popular in recent years. In this method, the slowness of a velocity field varying in both coordinates x and z is considered as being the sum of a slowness [Formula: see text], depending upon depth only, and a perturbation Δu of arbitrary shape but small compared with [Formula: see text]. The ray from the origin to any point can be easily traced for the laterally homogeneous part of the slowness, and the associated traveltime is quickly evaluated. The traveltime perturbation due to the lateral heterogeneities is approximated by the integral over the slowness perturbations along this raypath. The purpose of this note is to derive this approximation rigorously. Advantages of the method are the availability of an analytic expression for the time perturbation and the fact that no complicated ray tracing by solving differential equations is necessary. Consequently, the method allows several applications, e.g., in seismic modeling, migration, and tomography.