  Let N and P be smooth manifolds of dimensions n and p (n \geq p \geq 2)
respectively. Let \Omega(N,P) denote an open subspace of J^{infty}(N,P) which
consists of all regular jets and jets with prescribed singularities of types
A_{i}, D_{j} and E_{k}. An \Omega-regular map f:N \to P refers to a smooth map
having only singularities in \Omega(N,P) and satisfy the transversality
condition. We will prove the homotopy principle in the existence level for
\Omega-regular maps.
