The spectrum of the monoenergetic boundary value transport equation problem with general boundary conditions is studied. For the problems with special scattering cross-sections, the variational minima–maxima principles for the characteristic values (c.v.) are obtained. The dependence of the c.v. on the problem parameters (total and scattering cross–sections, boundary conditions, size and shape of the region) is studied. In some cases the result is the monotonicity, in some cases the result is the continuity, and in some cases the analyticity of the c.v. dependence on these parameters.