The dominant non-dimensional parameter for isodensity transverse jet flow is the mean jet-to-crossflow velocity ratio, R. In Part 1 (Megerian et al., J. Fluid Mech., vol. 593, 2007, p. 93), experimental results are presented for the behaviour of transverse-jet near-field shear-layer instabilities for velocity ratios in the range 1 < R ≤ 10. A local linear stability analysis is presented in this paper for the subrange R>4, using two different base flows for the transverse jet. The first analysis assumes the flow field to be described by a modified version of the potential flow solution of Coelho & Hunt (J. Fluid Mech., vol. 200, 1989, p. 95), in which the jet is enclosed by a vortex sheet. The second analysis assumes a continuous velocity model based on the same inviscid base flow; this analysis is valid for the larger values of Strouhal number expected to be typical of the most unstable disturbances, and allows prediction of a maximum spatial growth rate for the disturbances. In both approaches, results are obtained by expanding in inverse powers of R so that the free-jet results are obtained as R→∞. The results from both approaches agree in the moderately low-frequency regime. Maximum spatial growth rates and associated Strouhal numbers extracted from the second approach both increase with decreasing velocity ratio R, in agreement with the experimental results from Part 1 in the range 4<R≤10. The nominally axisymmetric mode is found to be the most unstable mode in the transverse-jet shear-layer near-field region, upstream of the end of the potential core. The overall agreement of theoretical and experimental results suggests that convective instability occurs in the transverse-jet shear layer for jet-to-crossflow velocity ratios above 4, and that the instability is strengthened as R is decreased.