  In this note we aim to study plane-wave limits of the solutions of type
II$^*$ superstring theories. We consider Freund-Rubin type $dS_5\times H^5$
solutions of type IIB$^*$ theory and obtain a new kind of plane-wave solutions,
we refer them as de Sitter plane-waves or Dpp-waves. Considering Hull's
time-like T-duality we are able to map the Dpp wave solution to maximally
supersymmetric Hpp-wave in IIB string theory and vice-versa.
