  We present a grid on non-linear convective type-II Cepheid models. The dense
model grids are computed for 0.6M_Sun and a range of metallicities
([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective
parameters are considered. The models cover the full temperature extent of the
classical instability strip, but are limited in luminosity; for the most
luminous models violent pulsation leads to the decoupling of the outermost
model shell. Hence, our survey reaches only the shortest period RV Tau domain.
  In the Hertzsprung-Russel diagram we detect two domains in which period
doubled pulsation is possible. The first extends through the BL Her domain and
low luminosity W Vir domain (pulsation periods ~2-6.5 d). The second domain
extends at higher luminosities (W Vir domain; periods >9.5d). Some models
within these domains display period-4 pulsation. We also detect very narrow
domains (~10 K wide) in which modulation of pulsation is possible. Another
interesting phenomenon we detect is double-mode pulsation in the fundamental
mode and in the fourth radial overtone. Fourth overtone is a surface mode,
trapped in the outer model layers. Single-mode pulsation in the fourth overtone
is also possible on the hot side of the classical instability strip. The origin
of the above phenomena is discussed. In particular, the role of resonances in
driving different pulsation dynamics as well as in shaping the morphology of
the radius variation curves is analysed.
