Analytic ray tracing is considerably less time consuming than numerical ray tracing. However, despite the advantage of speed, analytic ray tracing has a major limitation: the difficulty of including the effects on the ray path of horizontal gradients in electron density. In the past this difficulty has been addressed using ionospheric models whereby an effective tilt is introduced by displacing the center of the ionosphere from the center of the Earth. In this paper, ray equations for the ground range, phase path, group path, and divergent power loss are developed for a new two-dimensional analytic ray tracing technique, known as the segmented method for analytic ray tracing (SMART), which is able to deal with horizontal gradients in electron density. Ray tracing using two tilting methods are compared with ray tracing using SMART. Further, these results are compared with a numerical ray tracing program known as homing-in ray tracing (HIRT). ¿ 1999 American Geophysical Union