  We show that many important natural science models 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 essential
results concerning a particular model can be obtained as corollaries of general
theorems. However, in each case, the models have their own characteristics. The
article contains an overview of both potentially applicable methods, as well as
known results obtained for a particular model. In addition, we introduce new
models and obtain results for them.
