The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R³ . Let Ω^T ⊂ Ω be the subdomain filled by waves at the moment T, T _* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in Ω^T whereas for larger T < T_* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of Ω^T.