  We give two "lifting" constructions of strongly regular Cayley graphs. In the
first construction we "lift" a cyclotomic strongly regular graph by using a
subdifference set of the Singer difference set. The second construction uses
quadratic forms over finite fields and it is a common generalization of the
construction of the affine polar graphs \cite{CK86} and a construction of
strongly regular Cayley graphs given in \cite{FWXY}. The two constructions are
related in the following way: The second construction can be viewed as a
recursive construction, and the strongly regular Cayley graphs obtained from
the first construction can serve as starters for the second construction. We
also obtain association schemes from the second construction.
