  In this article we introduce and investigate a new class of rearrangement
invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue
Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are
some generalizations of known Grand Lebesgue Spaces (GLS).
  We consider the fundamental functions of CGLS, calculate its Boyd's indices,
obtain the norm boundedness some (regular and singular) operators in this
spaces, investigate the conjugate and associate spaces, show that CGLS obeys
the absolute continuous norm property etc.
