Persistent firing in response to a brief stimulus is a neural correlate of short-term memory in a variety of systems. In the oculomotor neural integrator, persistent firing that encodes eye position is maintained in response to transient saccadic eye-velocity commands. To a first approximation, firing rates in the integrator vary linearly with eye position. Thus, viewed across many cells, the pattern of persistent firing in the integrator may be constrained to a unique line of stable states. Here this idea was tested by examining the relationship between firing rates of simultaneously recorded neurons. Paired recordings were obtained in awake goldfish from neurons in hindbrain area I, an essential part of the horizontal eye-position integrator. During spontaneous eye movements consisting of sequential fixations at different horizontal positions, the pair relationship between the majority of cells on the same side of the integrator was not unique: for a given rate of one cell, the rate of the paired cell assumed different values that depended systematically on the preceding saccade history. This finding suggests that the set of persistent firing states that encode eye position is not constrained to a unique line, and that models with stable states restricted to a such a line need to be modified accordingly.