The kinetic evolution of a one-dimensional electrostatic plasma is discussed, comparing the different predictions of three kinetic models: the Vlasov model, the Lenard-Balescu model, and the exact transport model. The attention is focused on the Lenard-Balescu approach whose properties are studied in detail. The kinetic parameters present in the Lenard-Balescu collision operator are studied analytically and the kinetic equation with the Lenard-Balescu collision operator is solved numerically. The numerical solutions are compared with the results of an exact microscopic model and found in remarkable agreement. (C) 2002 American Institute of Physics.