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-The presented paper is focused on analysis of two methods of marker localization. The markers are passive RFID transponders (without or with identification chip) consisting of tuned LC circuit and being used to mark and trace underground networks such as cables and pipes. Localization of the marker is based on evaluation of signal amplitude received from the excited marker, i. e. it is RSSI based localization method. The excitation of marker can be periodically repeated or continuous. In the first case the localization process consists of two stages -excitation and receiving of marker damped oscillations, in the second case the amplitude of continuously generated excitation signal is decreased by vicinity of the marker. Both localization methods are mathematically analyzed by modeling of their circuits using differential equations. The results of analysis are used to compare both methods and to evaluate their suitability for practical utilization.