A generalization of Wigner's simple model for the distribution of nuclear level spacings is studied. It is based on a stochastic process which reproduces the correct joing probability distribution of N enerfy levels for small spacings. The case N=3, which includes the effect of the correlation between adjacent spacings, is discussed in detail. The resulting distribution and the correlation coefficient are compared with experimental data. No definite conclusion can be drawn except to say that the effect of the correlations on the spacing distributions on the spacing distribution is very small.