In this work, we consider control systems utilizing so-called Clegg integrators. A Clegg integrator is a linear integrator with reset mechanism whose describing function -38.1° has magnitude slope equivalent to that of a linear integrator, but with 52° less of phase lag. The potential advantages of using Clegg integrators has been demonstrated in the literature via simulations. However, except for describing function analysis, stability criteria specifically tailored to these feedback systems is missing. To address this omission we take two approaches by seeking to establish periodic behavior of the Clegg integrator’s reset action. In the second, we model the Clegg Integrator by a so-called Integral Quadratic Constraint (IQC). Both cases lead to stability criteria.