In this paper, after presenting a sum m ary of known results of the hom othetic m otions and the generalized ruled surfaces in the Euclidean space E n , A sym m etric lıom othetic motion of order k was defined and it was shown th a t a sym m etric hom othetic m otion of order k of E n is a reflection w ith respect to the (n--k—m)— dimensional subspace of E n . Moreover, the param eters of distribution, the pitehes, and the apex angles of th e moving and fixed ruled surfaces which are correspond to each other under the sym m etric hom othetic m otion of order k were given.