After configuring the proper electronic system to be used, the initial observations of the gamma-gamma coincidence approach were presented. These observations included hydrogen peak elimination, background and sum peak elimination, pulse pile up reduction, and two dimensional spectra. Three practical applications of the coincidence counting approach were presented in this work. The first application was performing elemental analysis for a mixture of radioisotopes using Library Least Squares (LLS). The LLS was applied to the coincidence data as well as the normal single detector data. The coincidence results showed to be much closer to the original activity values of the radioisotopes than the singles. In addition, the coincidence approach greatly reduced the background, summing, and pulse pile up effects. The second application was the two dimensional diagonal summing. The main advantages from this application were improving the peak resolution and greatly reducing the background (Compton Continuum). In addition, it was shown that different diagonal sums can be examined by use of the same set of data from the current electronic system (and software). The two dimensional diagonal summing was used for identifying coincidence schemes and for elemental analysis. The obtained spectra showed to be very promising and could be effectively used for these purposes. The third practical application was using a new NaI detector arrangement. The arrangement was designed to deal with the problem of the low detection probability of the high energy gamma rays of interest in the oil well logging industry. This arrangement consisted of two NaI detectors, one of which was a well type. The detectors were designed to fit in each other. Coincidence data were collected using this new arrangement. The results show that this new arrangement enhances the count rate in the coincidence data, thus increasing the Signal to Noise Ratio, as opposed to two separate detector setups. Finally, a Monte Carlo simulation attempt was made to try to predict the coincidence spectra. The attempt did not yield satisfactory results. It is our intent to continue pursuing coincidence simulation.