  We introduce two generalizations of the Jaynes-Cummings (JC) model for two
modes of oscillation. The first model is formed by two Jaynes-Cummings
interactions, while the second model is written as a simultaneous
Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of
its properties and obtain the energy spectrum and eigenfunctions of these
models by using the tilting transformation and the Perelomov number coherent
states of the two-dimensional harmonic oscillator. Moreover, as physical
applications, we connect these new models with two important and novelty
problems: The relativistic non-degenerate parametric amplifier and the
relativistic problem of two coupled oscillators.
