  For a special time-dependent homogeneous plane wave background that includes
a null singularity we construct the closed string propagators. We carry out the
summation over the oscillator modes and extract the worldsheet spacetime
structures of string propagators specially near the singularity. We construct
the closed string propagators in a time-independent smooth homogeneous plane
wave background characterized by the constant dilaton, the constant null NS-NS
field strength and the constant magnetic field. By expressing them in terms of
the hypergeometric function we reveal the background field dependences and the
worldsheet spacetime structures of string propagators. The conformal invariance
condition for the constant dilaton plays a role to simplify the expressions of
string propagators.
