The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domainΩ ⊂ R3 . Let ΩT ⊂ Ω be the subdomainfilled by waves at the moment T, T * the moment at which the waves fill the wholeof Ω. The following effect occurs: for small enoughT the system is approximately controllable in ΩT whereas forlarger T < T* a lack of controllability is possible. The subspace of unreachable statesis of finite dimension determined by topological characteristics of ΩT .