The second-order perturbation theory of convex-molecule fluids with pair interactions of the generalized Kihara type is considered. The double Yukawa potential function and the Laplace transform of the hard-sphere correlation function in the PY approximation are used to evaluate a part of the perturbation integral. The perturbation theory was applied to model systems of the LJ molecules and Kihara rod-like particles; calculated thermodynamic functions agree well with the corresponding Monte Carlo data and results from the Weeks-Chandler-Andersen theory. Characteristic parameters of several fluids with spherical and rod-like molecules were evaluated from the saturated liquid properties. Comparison with the corresponding parameters of the multicenter LJ potential is given.