The kinetics of the two-core configuration of the Argonaut reactor is examined. In this reactor two slightly subcritical slabs two feet apart are immersed in a large graphite reflector. The system achieves criticality by the small interaction due to exchange of thermal neutrons between the cores. The kinetic equations are derived by including an interaction term with the source terms of the thermal neutron diffusion equation, and writing a separate diffusion equation for each slab. This analysis accounts for observations that the ratio of flux levels in the two cores may depart considerably from unity although the reactor shows a single stable period. It is shown that the reactivity change which a rod in one core must introduce to restore criticality after a change is made in the other core is generally not equal in magnitude to that of the change which it compensates. Flux ratio as well as period must be known to determine the excess reactivities; conventional rod calibration data must be corrected for a progressive shift in flux ratio as reactivity is traded between rods. The rod drop method is discussed with two examples; a single relation does not suffice to describe the rod drop procedure. The single transfer function of a simple reactor system is replaced by a set of six transfer functions for the two-core system, two of which are derived for illustration. Even though an oscillator may be located midway between them, the amplitudes and phases of flux in the two cores will not agree except in the special situation of identical cores and equal flux levels. This complicates the problem of regulation.