  The paper is devoted to the problem of global exact controllability for a
wide class of neutral and mixed time-delay systems. We consider an equivalent
operator model in Hilbert space and formulate steering conditions of
controllable states as a vector moment problem. The existence of a basis of
eigenvectors of system operator allows to simplify substantially the form of
the moment problem. A change of control by a feedback law allows to modify the
system structure to guarantee the existence of a basis of eigenvectors of the
corresponding operator. We prove a criterion of exact controllability and
ascertain the precise critical time of controllability.
