The paper investigates the state space analysis of memristor based series and parallel RLCM circuits. The stability analysis was carried out with the help of eigenvalues formulation method, pole-zero plot and transient response of system. The state space analysis was successfully applied and eigenvalues of the two circuits were calculated. It was found that the system followed a negative real part of eigenvalues. The result clearly shows that addition of memristor in circuits does not alter the stability of the system. It was found that systems’ poles are located at left hand side of the S plane, which indicates a stable performance of system. It is clear that the eigenvalues have negative real part; hence the two systems are internally stable. Furthermore, the time and frequency domain resulting from both the systems suggest the stability of bounded input and bounded output (BIBO).