Logic elements endowed with memory are realized with two types of memristors: organic and inorganic ones. The organic devices are based on a polyaniline/polyethylene oxide heterostructure, while the inorganic ones are based on a Pt/Al 2 O 3/Ti heterostructure. The memristors are characterized by measuring cyclic voltage–current characteristics. They are then used to make AND gates showing memory abilities, exhibiting different behaviors. In the case of the inorganic devices the OFF/ON transitions are very fast when two inputs are applied simultaneously, while they are slow, with a gradual increase of the conductivity, in the case of the organic devices. The two types of devices are suggested as logic elements for future neuromorphic computers combining memory and processing properties.