Echo in telephones is generally undesirable but inevitable. There are two possible sources of echo in a telephone system. The impedance mismatch in hybrids generates network (electric) echo. The acoustic coupling between loudspeaker and microphone, in hands-free telephones, produces acoustic echo. Echo cancelers are used to control these echoes. In this thesis, we analyze the Least Mean Squares (LMS), Normalized LMS (NLMS), Recursive Least Squares (RLS), and Subband NLMS (SNLMS) algorithms, and evaluate their performance as acoustic and network echo cancelers. The algorithms are compared based on their convergence rate, steady state echo return loss (ERL), and complexity of implementation. While LMS is simple, its convergence rate is dependent on the eigenvalue spread of the signal. In particular, it converges slowly with speech as input. This problem is mitigated in NLMS. The complexity of NLMS is comparable to that of LMS. The convergence rate of RLS is independent of the eigenvalue spread, and it has the fastest convergence. On the other hand, RLS is highly computation intensive. Among the four algorithms considered here, SNLMS has the least complexity of implementation, as well as the slowest rate of convergence. Switching between the NLMS and SNLMS algorithms is used to achieve fast convergence with low computational requirements. For a given computational power, it is shown that switching between algorithms can give better performance than using either of the two algorithms exclusively, especially in rooms with long reverberation times. We also discuss various implementation issues associated with an integrated echo cancellation system, such as double-talk detection, finite precision effects, nonlinear processing, and howling detection and control. The use of a second adaptive filter is proposed, to reduce near-end ambient noise. Simulation results indicate that this approach can reduce the ambient noise by about 20 dB. A configuration is presented for the real time single-chip DSP implementation of acoustic and network echo cancelers, and an interface between the echo canceler and the telephone is proposed. Finally, some results obtained from simulations and implementations of individual modules, on the TMS320C31 and ADSP 2181 processors, are reported. The real time NLMS DSP implementations provide 15 dB of echo return loss. / Master of Science