[en] We present extensive molecular-dynamics (MD) computations of the time-dependent correlation functions of the classical one-component plasma over a wide range of thermodynamic states characterized by the dimensionless parameter GAMMA = e²/ak/subB/T, where a is the ion-sphere radius. The computed velocity autocorrelation functions exhibit marked oscillations for GAMMA approximately-greater-than 10 at a frequency close to the plasma frequency, showing the existence of strong coupling between single-particle and collective modes; this is confirmed by a standard memory-function analysis. The dynamical structure factor consists of very sharp peaks near the plasma frequency, up to wave vectors of order 1/a. The resulting dispersion curve exhibits negative dispersion for GAMMA approximately-greater-than 3. A simple memory-function analysis reproduces the MD data very well. At GAMMA = 152.4 our computations also provide evidence of well-defined shear modes. For large wave vectors a second, high-frequency transverse mode appears. From the correlation functions we have finally extracted estimates of the diffusion constant and the coefficient of shear viscosity. Near crystallization the shear viscosity has value which is unusually large compared with that of simple liquids near the triple point