<p>Conflict-controlled processes with non-fixed time are considered for the problem of the ray approach of a group of objects and motion camouflage. Two modifications of the method of resolving functions are proposed, in which the resolving functions do not depend on the moment of process completion. A strategy for the group quasi-parallel approach is defined, which, using the first modification of the method of resolving functions, ensures the successful completion of the process by a fixed end time and, in control examples, coincides with the well-known definition of parallel motion. An approach strategy for a group of ray-controlled objects is formulated, which justifies the well-known ray pursuit strategy. The second modification of the method of resolving functions ensures the ray approach of a group of objects with motion camouflage until the game’s fixed end time. The theoretical results of the study are illustrated with a control example.</p>