This paper is concerned with the problem of developing a family of locking protocols which employ both SHARED and EXCLUSIVE locks and which ensure the consistency of database systems that are accessed concurrently by a number of asynchronously running transactions. First, a general result concerning extensions of all protocols that employ EXCLUSIVE locks only to also employ SHARED locks is presented. Then a famdy of protocols apphcable to database systems that are modeled by directed acydtc graphs Is presented.