Lyapunov exponents have been known as an quantitive measure for characterization of dynamical instability and comprexibility and as a starting point for estabilishing thermo-chaotic relation. In this dessertation, we performed the molecular dynamics of mono- and triatomic molecular fluid systems to develop the thermo-chatic realtion between Kolmogorov-Sinai entropy (KS entropy) and self-diffusion pheonemenon. It is found in the case of mono-atomic fluids that KS entropy and the self-diffusion coefficients, when expressed in terms of the interparticle collision rate, has a simple power law, which is similar to Dzugutov`s suggestions in [Nature 381, 137] and [Phys. Rev. Lett. 81, 1762]. Our numerical results suggest a different type of thermo-chatoic relationship and it reads that the finite-size length scale of correlation of dynamical information is confidently involved from micrscopic region through to the thermodynamic level.Next we developed a molecular dynamics method to evaluate the full Lyapunov exponents of the two dimensional fluid system composed of tri-atomic molecules. The general trends and characteristic features of Lyapunov exponents and KS entropy, depending on density and intra-molecular angle, are examined. From the projection analysis of Lyapunov tangent vectors, we also found that the major contribution of dynamical instability comes from the fast divergence of momentum components in the phase-space trajectory.