We discuss theoretically the properties of an associative memory (a system that can retrieve a stored pattern that is similar to the input pattern) based on the ideal conductive properties of a molecularly linked nanosystem array. Two schemes are considered for the memory based on the gate potential modulation of the drainsource current through the array. In the first scheme, the basic units of the electric circuit are nanosystems (e.g., nanoparticles) arranged in a series array. Each nanosystem is assumed to have two states of conductances, G M and G m (G M . G m ), that can be tuned externally by the gate and backgate potentials. The bit sequence associated with a given pattern is stored as the components of a voltage vector. The input vector components are the gate voltages, and the stored vector components are the backgate voltages. The input pattern is compared with a given stored pattern by double-gating each nanosystem in the array with the respective components of the two vectors (the number of arrays is equal to the number of patterns to be stored). The individual conductances of the nanosystems in the array are high (G M ) when the input and stored vector components (bits) are equal and low (G m ) when they are different. The basis of the pattern recognition process is that the higher the number of bit coincidences, the higher the number of nanosystems in the array that are in states of high conductance and, therefore, the higher the drain-to-source current through the array. Alternatively, we consider also the properties of a second scheme in which the basic unit to be double-gated is the nanosystem array as a whole rather than a single nanosystem. Candidate experimental systems and simple circuit equations are considered for the two schemes that constitute preliminary steps toward future realizations of the associative memory using particular nanosystem arrays.