Mutual information is a useful extension of the correlation coecient to study the dependence
among multiple random processes. Hybrid processes are multivariate time series with some
components continuous time series and the rest point processes. Assessment of the strength
of the dependence structure amongst the components of hybrid processes are usually done by
various linear methods which often prove inadequate. In this paper mutual information is studied
for bivariate stationary hybrid processes. Results on convergence of the mutual information
estimates for bivariate time series are developed. It is shown that the mutual information
statistic can be super-optimal compared to the class of non-parametric estimates discussed in
Stone (1980).