The structure of the asymptotic log-likelihood ratio decision procedure for the discrimination of alternative stationary zero mean multivariate Gaussian processes is developed. The log-likelihood ratio statistic is shown to be asymptotically normally distributed. New time and frequency domain formulas for the conditional mean (The Kullback-Liebler information measure) and variance of the log-likelihood ratio statistic under the alternative hypotheses are given and the probability of misclassification is shown to be bounded exponentially with n, the number of observations.