In this paper the problem of the prior optimal control of the movement of the several controlling influences and controlability of the linear systems are considered. Complete controlling conditions of the nonstationary and stationary systems are given. It is shown that the system can be incompletely controlable due to each controlling influence, but due to their unity they can be completely controlable. For the solving problem of the prior optimal control of the movement, after building optimal controlling influences, the minimization of the quality criteria is done by the parameters, characterizing the priority of the controlling influences.