We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and high voltages are used to program the memristor's states. This way, as it was demonstrated in recent experiments, the state of memristors does not essentially change during analog mode operation. As an example of our approach, we have built several programmable analog circuits demonstrating memristor-based programming of threshold, gain and frequency.