Buchholz’s Ωμ+1-rules provide a major tool for the prooftheoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz . Mathematics Subject Classification (2010). 03B45, 03B70, 03F03, 03F05.