Model reference adaptive identifiers (MRAI) are designed with the assumption that the reference model M is strict positive real (SPR). The properties of MRAI with gradient algorithms have been well studied. In this paper we analyse the MRAI with least-square (LS) algorithms. It is found that a sufficient condition for the system stability is that M - 1/2 is SPR. A generic averaging technique is developed for the adaptive systems with periodic inputs. Then averaged systems of MRAI with the LS algorithm are formed. Simulation studies illustrate the properties of MRAI and verify the validity of the averaging approximation.