Let X 1 , ... , X r +1 be independent random variables having a standard gamma distribution with respective shape parameters α 1 , ... , α r +1 and define , i = 1, ... , r and , i = 1, ... , r where a ≠ 0 and b > 0 are constants. Then, ( Y 1 , ... , Y r ) and ( Z 1 , ... , Z r ) follow multivariate generalized beta type 1 and type 2 distributions, respectively. In this article several properties of these distributions are studied.