In QAM-type modems a hierarchy of synchronization problems are to be considered. First there is the problem of carrier synchronization, which deals with the generation of reference carrier with a phase closely matching that of the incoming signal. This reference carrier is used at the receiver to perform coherent demodulation operation resulting in the reconstruction of baseband data signal. A sampled data PLL is implemented to compensate the carrier phase- frequency offset. Second, the phase ambiguity of the received signal set requires special consideration in QAM-type signals. Examination of the signal constellation reveals that the receiver structure is in no way capable of distinguishing among the four different quadrants. This fourfold phase ambiguity requires differential encoding at the transmitter. Since the encoded data represents the phase changes in the original data rather than the phases themselves, therefore, this method of encoding resolves the phase ambiguity. Moreover, in modems operating at high data rates, adaptive equalization is an important function that deals with intersymbol interference. Two structures of the adaptive Least Mean Square (LMS) equalizers, two-sided transversal equalizer and one- sided transversal pulse decision feedback equalizer, are implemented to compensate channel distortion. Both for analytical purpose and to provide the theoretical basis for computer simulation of a 16-QAM modem, the idea of the Hilbert Transform Receiver is used in order to develop a baseband equivalent model of the passband system. A computer program written in C was developed to simulate a 16-QAM-type modem, having established the baseband equivalent model, with a bit rate equals to 9600 bps, utilizing a baseband equivalent telephone channel that combines both the transmitting and receiving shaping filters. This simulation allows for measurements of probability of symbol error versus SNR and learning curves of sampled data PLL and adaptive equalizers. Acquisition time in terms of symbols is given for different carrier phase-frequency offsets.