  The minimal models M(p',p) with p' > 2 have a unique (non-trivial) simple
current of conformal dimension h = (p' - 2) (p - 2) / 4. The representation
theory of the extended algebra defined by this simple current is investigated
in detail. All highest weight representations are proved to be irreducible:
There are thus no singular vectors in the extended theory. This has interesting
structural consequences. In particular, it leads to a recursive method for
computing the various terms appearing in the operator product expansion of the
simple current with itself. The simplest extended models are analysed in detail
and the question of equivalence of conformal field theories is carefully
examined.
