Abstract: Based on the energy conservation equation and L–S generalized thermoelasticity, the nonlinear coupled generalized thermoelasticity problem of inhomogeneous cylinders with material properties varying arbitrarily in the radial direction and depending on temperature is solved by using the state space technology and Newmark method. Through the numerical example analyses of functionally graded cylinders with temperature-independent (TID) and temperature-dependent (TD) materials, the temperature and the stress of cylinders varying in the radial direction and with time under the linear or nonlinear couplings are presented, and the correctness and validity of the solution in this paper are verified. The numerical results show that, considering the material properties depending on or independent of temperature and the coupling term in the energy conservation equation being linear or nonlinear, the temperature and the stress obtained are different in various degrees. The present solution can be readily applied to the generalized thermoelastic analysis of cylinders under different boundary conditions and initial conditions.