This paper deals with the flap control of unmanned aerial vehicles (UAVs) using shape memory alloy (SMA) actuators in an antagonistic configuration. The use of SMA actuators has the advantage of significant weight and cost reduction over the conventional actuation of the UAV flaps by electric motors or hydraulic actuators. In antagonistic configuration, two SMA actuators are used: one to rotate the flap clockwise and the other to rotate the flap counterclockwise. In this content, mathematical modeling of strain and power dissipation of SMA wire is obtained through characterization tests. Afterwards, the model of the antagonistic flap mechanism is derived. Later, based on these models both flap angle and power dissipation of the SMA wire are controlled in two different loops employing proportional-integral type and neural network based control schemes. The angle commands are converted to power commands through the outer loop controller later, which are updated using the error in the flap angle induced because of the indirect control and external effects. In this study, power consumption of the wire is introduced as a new internal feedback variable. Constructed simulation models are run and performance specifications of the proposed control systems are investigated. Consequently, it is shown that proposed controllers perform well in terms of achieving small tracking errors.