One-dimensional Lennard-Jones systems are investigated by molecular dynamics simulations. The full Lennard-Jones potential is compared to the repulsive Lennard-Jones potential. It is found that the pair correlation function and the normalized velocity autocorrelation function agree at high densities and high temperature. However, the diffusion coefficient indicates that the attractive potential introduces additional correlations into particle dynamics which are not reflected in the statics. These results are in agreement with three-dimensional studies.