[en] In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation