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Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of first-order logic that were recently introduced by H. Andreka et al. (1998). Guarded fixed point logics can also be viewed as the natural common extensions of the modal p-calculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIME-complete.