The complex analysis of strictly pseudoconvex domains in IE" is rather well known, especially since the boundary regularity properties of solutions of the inhomogeneous Cauchy-Riemann equations 8c~=fl on such domains have been described more and more precisely and important consequences from this have been derived (for a survey of the results in this direction known until 1972 (see [8]), more recent results are for instance contained in [15, 23]). In contrast to this situation, many fundamental questions with respect to the most "natural" domains of complex analysis, namely arbitrary pseudoconvex domains in ~ ' , are still open. What is the reason for this discrepancy? One possible answer to this question can be seen in the following observation. In almost all important proofs concerning the analysis of strictly pseudoconvex domains, at least one out of three elementary properties of these domains play a fundamental role. They are: 1) Strict pseudoconvexity is stable with respect to small C2-perturbations. 2) A strictly pseudoconvex domain is locally biholomorphically equivalent to strictly convex domains. 3) If ( 2 c c ~ " is strictly pseudoconvex with a smooth C2-boundary, then there is a neighborhood U of ~ and a strictly plurisubharmonic C 2 function p on U such that dp(p):t=O for peb~2 and