This paper summarizes the important aspects of digital modem (modulator-demodulator) design for linear and nonlinear satellite channels using time-division multiple access (TDMA). The modem performance degradations caused by transmission anomalies, such as amplitude and delay distortions, effects of single and cascaded nonlinearities, and band-limiting effects in nonlinear channels, have been examined using the test data gathered from various field test programs using INTELSAT IV satellites and laboratory simulations using both INTELSAT IV and INTELSAT V parameters. A systematic methodology has been prescribed to reduce the effect of transmission anomalies on the performance of the modems. This paper consists of three main sections; essential features of TDMA modem design, transmission anomalies and their effects on modem performance, and optimization of modem performance in the presence of transmission deviations. The latter includes a brief description of an advanced maximum-likelihood sequence detection (MLSD) technique for application to the nonlinear channel.