The comparison of the means of two populations on the basis of two independent samples is one of the oldest problems in statistics. Indeed, it has been a testing ground for many methods of inference as well as for a variety of analytic approaches to practical problems. The univariate problem was first studied by Behrens (1929) and his solution was presented by Fisher (1935) in terms of the fiducial theory. Welch studied it in the confidence theory framework and provided an 'approximate degrees of freedom' solution as well as an asymptotic series solution (1936, 1947). Many others have investigated this topic and various methods of approach were also suggested by Jeifreys (1940), Scheff6 (1943), McCullough, Gurland & Rosenberg (1960), Banerjee (1961), and Savage (1961). In the multivariate extension of the Behrens-Fisher problem, Bennett (1951) has extended the Scheff6 solution, and James (1954) the Welch series solution. The present paper studies an extension of the Welch 'approximate degrees of freedom' (APDF) solution provided by Tukey (1959), and discusses the results of a Monte Carlo sampling study on this new APDF solution and its comparison with the James series solution.