\noindent ``Integrability meeting ENS/IPhT'' \\ \\ We consider a problem of Bethe vectors scalar products of the models solvable by the (nested) algebraic Bethe ansatz. For the models with gl(2) symmetry or its q-deformation, the scalar products can be calculated straightforwardly via the standard arguments of the algebraic Bethe ansatz. However, for the models with higher rank symmetry, the technical complexity of such a calculation increases immensely. We suggest a new method based on the coproduct properties of the Bethe vectors. We illustrate this method by the example of the scalar products in the gl(2) based models. \\ \\ (IPhT organizer: Ivan Kostov)