In this talk we are going to discuss the problem of travelling capillary-gravity waves in the shallow water regime. The governing equations are provided by the fully nonlinear Serre-Green-Naghdi system completed with the surface tension term. In the first time we will discuss the formulation for travelling waves based on the conservation laws. Then, we will show that these solutions will belong to a family of algebraic curves parametrized by the Froud and Bond numbers. Finally, we will employ some methods of the algebraic geometry in order to classify the possible topologies of these curves depending on the values of physical parameters.