Let {(xi:, Yi:), i = 1, …, n) be the observed data, where xi:is a real vector of lengthkand Yi:, i = 1, …, n a sequence of random variables (r.v.'s). The minimum distance (M.D.) estimators considered here are obtained by minimizing with respect to t the integral dH(y) of the R2norm of the following functionals A-½n[d]i=1:xi:{IYi:-xi:t[d]y] -I[-Yi+ xi:t[d]y]} and A1:½n[d]i=1::(xi:- x)I[Yiy + xit], where A and Al:are matricies such that the inverse of their square root exists. The existence of some of these estimators of thek-dimensional slope parameters under the multiple linear