  We show a theorem proving that a non-local bosonic field upon a covariant
interaction with a confining gauge field undergoes the confinement of its
degrees of freedom present in the free theory changing completely the physical
mass spectrum following Kugo-Ojima criterion. This is applicable to an infinite
number of excitations of the bosonic field including ghosts whereas we pay
special attention to the modes with the complex conjugate masses, states
appearing in the string field theory motivated infinite-derivative models. The
same recipe will obviously work for the Lee-Wick models.
