  Although the driving mechanism acting in beta Cephei pulsators is well known
(e.g. Dziembowski & Pamyatnykh 1993), problems concerning identification of
amplitude limitation mechanism and non-uniform filling of the theoretical
instability strip, remain to be solved. In the present analysis, these problems
are addressed by non-linear modelling of radial pulsations of these stars. In
this approach radial modes are treated as representative for all acoustic
oscillations.
  Several models of different masses and metallicities were converged to limit
cycles through Stellingwerf (1974) relaxation technique. Resulting peak-to-peak
amplitudes are of order of DeltaV=0.3 mag. Such amplitudes are significantly
larger than those observed in beta Cephei pulsators. Assuming that all acoustic
modes are similar, we show that collective saturation of the driving mechanism
by several acoustic modes can easily lower predicted saturation amplitudes to
the observed level. Our calculations predict significant decrease of saturation
amplitudes as we go to high mass/high luminosity models. However, this effect
is not strong enough to explain scarcity of high mass beta Cephei variables.
  We also discuss robust double-mode behaviour, encountered in our radiative
models. On a single evolutionary track we identify two double-mode domains with
two different mechanisms resposible for double-mode behaviour. The non-resonant
double-mode domain separates first overtone and fundamental mode pulsation
domains. The resonant double-mode domain appears in the middle of the first
overtone pulsation domain. Its origin can be traced to the
2omega_1=omega_0+omega_2 parametric resonance, which destabilizes the first
overtone limit cycle.
