  Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and
Lorentz spaces. They have been studied by many authors, including Masty\l o,
Maligranda, and Kami\'nska. In this paper, we consider the problem of comparing
the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for
them to be equivalent. As a corollary, we give necessary and sufficient
conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space,
extending results of Lorentz and Raynaud. We also give an example of a
rearrangement invariant space that is not an Orlicz-Lorentz space.
