Two parallel circular jets, in inviscid incompressible flow, with uniform axial velocity of the same magnitude and direction are placed near to one another, resulting in a strongly coupled field. A given (small) wavenumber in the axial direction is taken and a dispersion relation is found relating the frequency and wavenumber for a given disturbance mode, along with the velocity potentials within and exterior to the jets. The problem is tackled analytically using bipolar coordinates and asymptotic forms for the dispersion relation are found in the small-separation and large-separation limits. Results are then compared with the corresponding two-dimensional problem for plane jets. It is concluded that close-proximity interactions greatly destabilize the varicose mode of the coupled jet, and greatly stabilize the sinuous mode.