  We study the structure of the spectrum of a two-level quantum system weakly
coupled to a boson field (spin-boson model). Our analysis allows to avoid the
cutoff in the number of bosons, if their spectrum is bounded below by a
positive constant. We show that, for small coupling constant, the lower part of
the spectrum of the spin-boson Hamiltonian contains (one or two) isolated
eigenvalues and (respectively, one or two) manifolds of atom $+ 1$-boson states
indexed by the boson momentum $q$. The dispersion laws and generalized
eigenfunctions of the latter are calculated.
