This paper studies various dynamical features of fixed delta modulator (∆-M) and adaptive ∆-M. Stability conditions of both systems are formulated using the theory of quasi-sliding mode. Further, the existence of periodic solutions for fixed delta modulator (∆-M) and its adaptive counterpart, with steady-state inputs and certain parameter values, are investigated. Our results show that fixed ∆-M converges to the periodic-2 orbit whereas adaptive ∆-M converges to periodic-4 orbit. To validate our theoretical results, we consider extensive simulation examples with various behaviors for both systems.