It is shown that the optimal traj ectories in the linear problem of optimal control with a quadratic functional and a large parameter accompanying the control are close, in a certain sense, to the solutions of a specially constructed problem of the same type but of lower dimension. The controls in this new problem are the “rapid” components of the phase variables. In the applications, the mathematical model of the controlled object may contain large gain coefficients of the order of e~1 (e > 0 is a small parameter). Such models are singularly -perturbed [1], some of their motions are rapid, and some are slow. This was pointed out, in particular, by Gerashchenko in [2] where the problem of separating the motions in a closed control system with a large gain coefficient accompanying the control was discussed. Problems of optimal control with differential constraints of this type are usually solved in the following manner: equations containing e-1 are multiplied by e, and then assumed e = 0 whereupon the whole control vector or some of its coordinates vanish and the corresponding phase variables become the controls in the resulting problem of lower dimension. For example, the computations in the problem of controlling the flight of a rocket in vacuo (plane case) which was shown to the author by N, N. Moiseev, are carried out with the rotation about the center of mass neglected, i. e. the phase variable represented by the angle related to the direction of thrust is regarded as the control, and the control consisting of the torsional moment is neglected (see also [3]). The above approach is substantiated using, as an example, the problem of analytic construction of a regulator of state.