We develop a molecular dynamic method to evaluate the full Lyapunov spectrum for two-dimensonal fluids composed of rigid diatomic molecules. The Lyapunov spectra are obtained for 18 rigid diatomic molecules for various bond lengths d(10(-3)less than or equal to d less than or equal to 1.0) in two dimensions with periodic boundary conditions, and interacting with Hoover and Weeks-Chandler-Anderson short-range repulsive forces. The general trends and characteristic features of the Lyapunov spectra are examined for both potentials. Our results are compared with those obtained from I. Borzsak et al. [Phys. Rev. E 53, 3694 (1996)], whose model uses the Lagrange multiplier method. [S1063-651X(98)06612-4].