This paper investigates memristor based demodulators and proposes new circuit designs for Binary Frequency Shift Keying (BFSK) and circular 8-Quadrature Amplitude Modulation (QAM) demodulators using two memristors at most. The proposed designs consider utilizing the unique features of the memristor element, crucially, its variable average memristance with the amplitude, phase and frequency of the sinusoidal excitation signal. The proposed QAM demodulator eliminates the need for any carrier recovery circuits. Moreover, both of the proposed QAM and BFSK demodulators are all passive circuits. The designs are further verified by the transient circuit simulations using the memristor linear dopant drift model.