The effect of wheel-rail contacts and track gauge variation to hunting behaviours has been investigated using a comprehensive three-piece bogie wagon non-linear dynamics model. The determination of critical hunting speed is through the simulations using the decreasing vehicle speed and the constant speeds. It is found that the critical hunting speed is corresponding to the one at which the cycle amplitude starts to reduce. Based on constant speed simulations, a critical hunting speed with the accuracy of 0.2km/h can be determined. The key influence on three-piece wagon hunting appears to be the rolling radius difference at flange and as track gauge increases the stability of a three-piece wagon will decrease due to resulting increases in the rolling radius difference at flange. The widening track gauge will significantly increase the hunting cycle amplitude and decrease the hunting cycle frequency.