Polydiapirs (domes-in-domes) result from the evolution of a multiwavelength Rayleigh-Taylor (gravitational) instability. The present work investigates the initiation and development of polydiapirs by means of two-dimensional finite-difference models of gravitationally unstable triple-layered sequences of Newtonian fluids. The values of viscosities, thicknesses and densities were systematically varied for selected examples. In triple-layered sequences, only two types of density stratification are likely to result in multiwavelength instabilities that will eventually develop into polydiapiric structures. The limiting factors and evolution of such structures were studied for both these types of density stratifications. Finite-difference calculations on models with physical parameters appropriate to evaporitic sequences and covered by a viscous clastic overburden showed that a very small downward density decrease in the evaporitic source may cause an internal overturn that will compete with the main overturn between source and overburden. This may lead to the development of sequential or simultaneous polydiapirs. The mature polydiapirs in the models exhibit spines, curtain folds, pendant repetitions of the source layers inside the large diapirs, and anomalous interdiapiric distances. All these features are known in natural salt diapirs suggesting that polydiapirs may be far more common in nature than hitherto recognized.