Let V be an n-dimensional vector space over GF(q) and for integers k⩾t>0 let mq(n, k, t) denote the maximum possible number of subspaces in a t-intersecting family of k-dimensional subspaces of V, i.e., dim F ∩ F′ ⩾ t holds for all F, F′ ϵ . It is shown that for n⩾2k−t while for n⩽2k−t trivially holds.