  In this note we shall construct, in the framework of relativistic quantum
mechanics, the Poincare-invariant motion equations with realistic mass spectra.
These equations describe a system with mass spectra of the form $m^2=a^2+b^2
s(s+1)$, where a and b are arbitrary parameters. Such equations are obtained by
a reduction of the motion equation for two particles to a one-particle equation
which describes the particle in various mass and spin states. It we impose a
certain condition on the wave function of the derived equation, such an
equation describes the free motion of a fixed-mass particle with arbitrary (but
fixed) spin s.
