Rotating elements, including gears, are one of the most problematic elements in machinery. It is not preferable to monitor their condition visually considering time and money is required to take apart the machine to observe the parts. Monitoring of gears is important because the failure of such elements can cause major damage to machinery. A few non-invasive methods are proposed, however vibration analysis is, so far, the most efficient way to monitor the condition of the gear. Vibrations are caused by the continuous contact between the two rotating gears. When a fault occurs, the signal is modified in different ways depending on the type of fault - distributed or local. Many fault detection methods are effective for one type of fault or the other. In this thesis, several methods are proposed with the objective of finding an efficient method for both types of faults. The calculus enhanced energy operator (CEEO), previously designed for bearing fault detection, is proposed here for the first time on gears. Two other methods, the EO123 and EO23, are derived based on the original energy operator. The proposed methods are filter free, simple and can handle a certain level of noise and interference. With the exception of low rotational frequencies of the gears, it can be concluded from simulated and experimentally-obtained signals that the CEEO method can handle noise better than the other proposed methods and that the EO23 method can handle interference better than the others. Different conditions determine the effectiveness of the methods.