Summary: We consider the matrix Schrödinger operator \(-D+V(x)\) in the layer \(\mathbf R^{d-1}\times (0,T)\), \(d\geq 2\). The potential \(V\) is assumed to be periodic along the layer. We supply the operator with appropriate boundary conditions. The Dirichlet and Neumann boundary conditions, the third boundary condition with periodic coefficients, and quasiperiodic conditions are allowed. The spectra of the corresponding operators are shown to be free of eigenvalues. In the self-adjoint case, the spectrum is absolutely continuous.