The kinematic aspect of surveillance-evasion is studied with a deterministic differential game model. The model considers a pursuer with limitations on both speed and maneuverability (turning radius) and an evader with only a speed limitation. Conditions are developed for the pursuer to be able to maintain contact indefinitely. The results of this research modify previously published results on this problem. Shortcomings of previous work are discussed including the fact that the surveillance-evasion problem has not been solved for an arbitrary detection region. Related parts of the solution to Isaacs' homicidal chauffeur game and its one-sided counterpart are developed as background material. Some known allocation of effort in search theory results are derived by the Pontryagin maximum principle.