Static and dynamic structure factors and various transport coefficients are computed for a Lennard-Jones model of a binary fluid (A,B) with a symmetrical miscibility gap, varying both the temperature and relative concentration of the mixture. The model is first equilibrated by a semi-grandcanonical Monte Carlo method, choosing the temperature and chemical potential difference Deltamu between the two species as the given independent variables. Varying for Deltamu=0 the temperature and particle number N over a wide range, the location of the coexistence curve in the thermodynamic limit is estimated. Well-equilibrated configurations from these Monte Carlo runs are used as initial states for microcanonical molecular dynamics runs, in order to study the microscopic structure and the behavior of transport coefficients as well as dynamic correlation functions along the coexistence curve. Dynamic structure factors S-alphabeta(q,t) [and the corresponding static functions S-alphabeta(q)] are recorded (alpha,betais an element ofA,B), q being the wave number and t the time, as well as the mean square displacements of the particles (to obtain the self-diffusion constants D-A, D-B) and transport coefficients describing collective transport, such as the interdiffusion constant and the shear viscosity. The minority species is found to diffuse a bit faster than the majority species. Despite the presence of strong concentration fluctuations in the system the Stokes-Einstein relation is a reasonable approximation. (C) 2003 American Institute of Physics.