The data arenunivariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type ofm-dependence occurs. General expressions are developed that depend onn, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual observations. These results seem to be in a form that is satisfactory for practical applications, and a rule is given for deciding whennis large enough for their use. Also, a basis is furnished for deciding on the suitability of the model from the characteristics of the experimental situation, and consistent estimation of the average of the cdf's is considered. In practice, the asymptotic distributions that occur for the case of samples from continuous populations also seem to frequently occur for nonsample cases involving data that are not necessarily continuous. Some reasons are given which tend to explain the frequent occurrence of these types of asymptotic distributions.