  The classical Grauert and Ramspott theorems constitute the foundation of the
Oka principle on Stein spaces. In this paper we establish analogous results on
the maximal ideal space $M(H^\infty)$ of the Banach algebra $H^\infty$ of
bounded holomorphic functions on the open unit disk $\mathbb D\subset\mathbb
C$. We illustrate our results by some examples and applications to the theory
of operator-valued $H^\infty$ functions.
