  We present the hydrodynamic BL Herculis-type models which display a long-term
modulation of pulsation amplitudes and phases. The modulation is either
strictly periodic or it is quasi-periodic, with the modulation period and
modulation pattern varying from one cycle to the other. Such behaviour has not
been observed in any BL Her variable so far, however, it is a common property
of their lower luminosity siblings - RR Lyrae variables showing the Blazhko
effect. These models provide a support for the recent mechanism proposed by
Buchler & Kollath to explain this still mysterious phenomenon. In their model,
a half-integer resonance that causes the period doubling effect, discovered
recently in the Blazhko RR Lyrae stars, is responsible for the modulation of
the pulsation as well. Although our models are more luminous than is
appropriate for RR Lyrae stars, they clearly demonstrate, through direct
hydrodynamic computation, that the mechanism can indeed be operational.
  Of great importance are models which show quasi-periodic modulation - a
phenomenon observed in Blazhko RR Lyrae stars. Our models coupled with the
analysis of the amplitude equations show that such behaviour may be caused by
the dynamical evolution occurring in the close proximity of the unstable single
periodic saddle point.
