© 2018, EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature. Abstract: We study and exactly solve the two-photon and k-photon Jaynes–Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the SU(2) group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model. Graphical abstract: [Figure not available: see fulltext.].