We investigate the mutual trapping of intense fundamental and second-harmonic waves propagating in materials with second-order nonlinearity. Consistent with Menyuk’s robustness hypothesis of solitons, we numerically observe that solitonlike waves emerge from the input signal over a wide range of excitation conditions for both signs of the phase mismatch and in the presence of moderate linear walk-off between the interacting waves. The solitons exist above a threshold intensity and in general arise as oscillating states. The trapping of the waves is governed by the sign of the phase mismatch, by the beam or pulse width, and by the absolute value of the phase mismatch through the ratios among the characteristic lengths of the wave evolution, namely, the diffractive, walk-off, and nonlinear interaction lengths.