The authors present a systematic method of investigating the dynamics of homogeneous multidimensional cosmological models. The method is based on the full classification of homogeneous multidimensional Kaluza-Klein models. The space sections are homogeneous diffeomorphic to the coset space G/H, where H is a discrete subgroup (dim(H)=0). Here they set H=I (the identity group) and consider the group manifold MD+3=G3+D as a model space. Additionally, they assume that MD+3=M3*BD and that the spatial metric is decomposable, i.e. equivalent to independent metrics on the macrospace factor manifold M3 and microspace BD which are orthogonal to each other. The spatial metric matrix g has then a block diagonal form g=(g3,gD). They further assume that metric gD is also in block diagonal form with matrix blocks in each microspace sector. They reduce the investigation of dynamics to the investigation of multidimensional dynamical systems and then draw some general conclusions about chaotic behaviour and genericity of homogeneous multidimensional cosmological models.