We present a grid on non-linear convective type-II Cepheid models .
The dense model grids are computed for 0.6 { } { M } _ { \odot } and a range of metallicities ( { [ Fe / H ] } = -2.0 , -1.5 , -1.0 ) , and for 0.8 { } { M } _ { \odot } ( { [ 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 \sim 2 - 6.5 d ) .
The second domain extends at higher luminosities ( W Vir domain ; periods > 9.5 d ) .
Some models within these domains display period-4 pulsation .
We also detect very narrow domains ( \sim 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 .