The instability of a vortex‐pair to infinitesimal disturbances is studied in the inviscid and incompressible fluid approximations. The cores of the vortices contain uniform axial‐velocity jets of fluid density different from that of the surrounding medium. In one model a nonrotating core with surrounding potential vortex is assumed, and in the other a uniformly rotating core. In the lowest order of a perturbation parameter, denoting the ratio of vortex core radius to the distance between the vortices, the long‐wavelength symmetric amplification factor of a vortex‐pair decreases with increasing jet axial‐velocity in either model, with decreasing core density in a rotating core model, and with increasing core density in nonrotating core model. The vortex‐pair is more unstable to negative mode of deformation than to the positive mode in the presence of an axial jet in both models considered. The surface tension has a destabilizing effect on the vortex pair in the long‐wavelength approximations. The effect of core density and jet axial velocity on long‐wavelength symmetric amplification factors of the vortex pair in higher orders of perturbation parameters have also been outlined.