In the transmission of digital data at a relatively high rate over a particular limited band channel, it is normally necessary to employ an equalizer at the receiver in order to correct the signal distortion introduced by the channel .The intersymbol interference (ISI) leads to large error probability at the received signal if it is not minimized .The possible solutions for minimizing the effect of ISI are equalization techniques. Maximum Likelihood Sequence Estimation (MLSE) implemented with Viterbi algorithm is the optimal equalizer for this ISI problem since it minimizes the sequence of error rate. Decision Feedback Equalizer (DFE) and Near Maximum Likelihood Sequence Estimation Algorithms are presented. A new algorithm has suggested which improves the performance of nonlinear equalizer with perturbation, and it depicted in detail. The nonlinear equalizer with perturbation could be applied to sampling delay 1, and 2. All the reduced complexity algorithms have been tested by computer simulation; their results are compared with each other, where different tolerances to additive white Gaussian noise are chosen over different telephone channels. The results of the computer simulation show that the improved non- linear equalizer with perturbation algorithm gives an enhancement in the receiver performance of different values (0.5, 1, 0.8, and 1.45 dB) in different telephone circuit channels and (0.9, and 0.5 dB) in mobile channel compared with the Decision Feedback Equalizer (DFE). Relatively to these results of the improved nonlinear equalizer with perturbation, it may be used in the receiver’s detector.