The bandwidth of angle-tuned optical parametric oscillators, in some cases, is limited by the noncolinear interaction of the pump, signal, and idler beams, which results when the non-linear material is rotated relative to the pump beam. The decreased beam overlap reduces the parametric gain and increases the pump power threshold. To determine this bandwidth, a theoretical expression for the threshold is derived in the near field limit taking into account double refraction for a noncolinear interaction. Angle tuning can be done by 1) rotating the crystal and mirrors as a unit, or by 2) rotating the crystal only. Expressions for determining the tuning rate and threshold increase for both tuning methods are derived. Angle tuning about the 90° phase-matching axis in LiNbO3(the low-threshold design) is shown to be not practical. A combination of step temperature tuning and voltage fine tuning is found to be most practical in this case. A wide-band oscillator with a small threshold increase is shown to be possible by angle tuning about an axis not parallel to a crystal axis. The threshold increases very little if the oscillator is tuned by rotating only the crystal inside an optical cavity made of one curved and one flat mirror.