  We construct monads for framed torsion-free sheaves on blow-ups of the
complex projective plane at finitely many distinct points. Using these monads
we prove that the moduli space of such sheaves is a smooth algebraic variety.
Moreover we construct monads for families of such sheaves parameterized by a
noetherian scheme S of finite type. A universal monad on the moduli space is
introduced and used to prove that the moduli space is fine.
