  We define an equivalence relation among coherent sheaves on a projective
variety called biliaison. We prove the existence of sheaves that are minimal in
a biliaison class in a suitable sense, and show that all sheaves in the same
class can be obtained from a minimal one using certain deformations and other
basic moves. Our results generalize the main theorems of liaison theory of
subvarieties to sheaves, and provide a framework to study sheaves and
subvarieties simultaneously.
