<p>Conflict-controlled processes with non-fixed time are considered, for which two modifications of the resolving function method are proposed. A quasi-parallel convergence strategy is defined, which, with the help of the first modification of the resolving function method, ensures the successful completion of the process by a fixed end time and, in control examples, coincides with the known definition of parallel motion. The second modification of the resolving function method ensures convergence along a ray to a fixed end time of the game. A motion camouflage strategy is formulated, which is an important special case of the strategy of pursuit along a ray and is of independent interest. The theoretical results of the work are illustrated by a control example.</p>