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