A graph G is called (k, n)-pendant tree-connected, iff for any subset A of the vertex set of G with cardinality k there exist n edge-disjoint trees T1,…, Tn which contain A as set of endvertices and are vertex-disjoint with the exception of A. This is a specialization of the tree-connectivity introduced in (M. Hager, Tree-connectivity in graphs, submitted) and includes the usual vertex-connectivity for k = 2. Necessary and sufficient conditions are given for a graph to be (k, n)-pendant tree-connected proving that κ(G)≥2n(k + 1) implies the (k, n)-pendant tree-connectivity and k + n + 1 is a lower bound for this implication. Then we handle the case (3,2) showing that nonplanar graphs G with κ(G)≥4, such that G-{e} for some edge e is planar, are (3,2)-pendant tree-connected.