||Convective and absolute nature of instabilities in nondegenerate optical parametric oscillators with large transverse section, for negative detunings and in the presence of walkoff, is examined. The asymptotic response of the signal and idler fields to a transverse localized two-dimensional perturbation is evaluated. The presence of walkoff breaks the rotational symmetry in the transverse plane, and the system, at the absolute instability threshold, selects traveling waves propagating in the walkoff direction among an infinity of unstable spatiotemporal modes. We show that in optical parametric oscillators (OPO's) with negative detunings, contrary to the case of positive detunings, the walkoff shrinks the region of convective instabilities, and even may suppress the convective/absolute transition. Hence, in a certain range of parameters, signal field envelopes in the form of wave packets of zero group velocity are found where the instability is absolute at the onset, although the walkoff is present. We also show that nonlinear pattern selection is ruled by the cross-coupling terms appearing in the asymmetric coupled Ginzburg-Landau equations derived near-threshold of the signal and idler generation. The numerical solutions of the original OPO equations confirm the analytical predictions for the values of the instability thresholds and the corresponding selected patterns.