We present a grid of nonlinear convective pulsation models of type-II Cepheids: BL Her stars, W Vir stars and RV Tau stars. The models have 0.6M⊙ and cover a wide range of luminosities, effective temperatures and chemical compositions. The most important result is the detection of two domains in the HR diagram, in which period doubling effect is present. First domain, with pulsation periods in between 2 d and 5.5 d, was also detected in earlier radiative computations. The first star showing the period doubling effect with period in the predicted range (≈ 2.4 d) was discovered recently. The second domain extends for periods longer than 9.5 d but so far no period-doubled type-II Cepheid that could be associated with this domain was discovered. We also detect very small domains in which modulation of pulsation is possible. The origin of these phenomena may be assocaited with half-integer resonances between radial pulsation modes. In the most luminous models a dynamical instability is detected, which indicates that pulsation driven mass loss is important process occurring in type-II Cepheids.