This paper addresses combined location/routing problems defined on trees. Several problems are studied, which consider service demand both at the vertices and the edges of the input tree. Greedy type optimal heuristics are presented for the cases when all vertices have to be visited and facilities have no set-up costs. Facilities set-up costs can also be handled with interchange heuristics of low order. More general problems where not all vertices have to be necessarily visited require more sophisticated solution methods. Low order optimal algorithms based on recursions are proposed for such problems.