We study the BPS states of non-critical strings which arise for zero s
ize instantons of exceptional groups. This is accomplished by using F-
theory and M-theory duals and by employing mirror symmetry to compute
the degeneracy of membranes wrapped around 2-cycles of the Calabi-Yau
threefold. We find evidence for a number of novel physical phenomena,
including having infinitely many light states with the first lightest
state including a nearly massless gravitino.