Asymmetric limit cycles and input-output properties of relay feedback systems with integrating plants are studied in the technical note. It is noted that an integrating plant introduces significantly different dynamics, so that a different than traditional system representation is needed to obtain a fixed point of Poincare map. Conditions of orbital asymptotic stability are obtained. The infinite set of possible periodic solutions and transfer characteristics is presented in the form of the locus of a perturbed relay system (LPRS). A formula of LPRS is derived. An example of analysis of oscillations and transfer properties is given.