Аннотация:We show that many important models of natural science in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some important results concerning a particular model can be obtained as corollaries of general theorems. However, in each case, the models have their characteristics. The paper contains an overview of both methods that are potentially applicable to such cases, as well as known results obtained for a particular model. In addition, we introduce new models and obtain results for them.