  We consider AdS/CFT correspondence for time-dependent \II B backgrounds in
this paper. The supergravity solutions we construct are supersymmetric pp-waves
on AdS and may have null singularity in the bulk. The dual gauge theory is also
constructed explicitly and is given by a time-dependent supersymmetric
Yang-Mills theory living on the boundary. Apart from the usual terms that are
dictated by the geometry, our gauge theory action features also a
time-dependent axion coupling and a time-dependent gauge coupling. Both of
which are necessary due to the presence of a nontrivial dilaton and axion
profile in the supergravity solution. The proposal is supported by a precise
matching in the symmetries and functional dependence on the null coordinate of
the two theories. As applications, we show how the bulk Einstein equation may
be reproduced from the gauge theory. We also study and compare the behaviour of
the field theory two-point functions. We find that the two-point function
computed by using duality is different from that by doing a direct field theory
computation. In particular the spacetime singularity is not seen in our gauge
theory result, suggesting that the spacetime singularity may be resolved in the
gauge theory.
