  We consider M theory 5-branes with compact transverse dimensions. In certain
limits the theory on the 5-brane decouples and defines ``little string
theories'' in 5+1 dimensions. We show that the familiar structure of
IIA/IIB,M,F- theory in 10,11,12 dimensions respectively has a perfect parallel
in a theory of strings and membranes in 6,7,8 dimensions. We call these
theories $a/b,m,f$ theories. They have a coupling constant but no gravity. This
construction clarifies some mysteries in F-theory and leads to several
speculations about the phase structure of M theory.
