  In this paper we obtain strings that propagate in the quantized pp-wave
backgrounds. We can obtain these strings from the solutions of membrane. The
other way is the propagation of a massless string in a spacetime with two time
dimensions. This string sweeps a worldvolume, which enables us to obtain other
strings in the quantized pp-wave backgrounds in the spacetime with one time
direction. The associated algebras and Hamiltonians of these massive strings
will be studied.
