This paper deals with the performance comparison of adaptive equalization algorithm, MMA and SCA, that is used for the minimization of the distortion and noise effect in the communication channel.. The transmitting signal will be distorted and received due to the nonlinearties of magnitude and phase transfer characteristics of communication channel, the compensation of it by using the self adaptive equalizer. The constant modulus has important metric in the self adaptive equalizer, the MMA uses the 2nd and 4th high order statistics of transmitting signal, the SCA uses the 2nd order statistics of transmitting signal only in order to the calculation of it. We compared to the compensation performance of the MMA and SCA by the computer simulation that are possible to the compensation of the two kinds of transfer characteristics at same times by the relatively simple arithmatic operation. We used to the recovered constellation, residual isi and MSE, SER that are the essential index for the comparison of the adaptive equalizer. The result of performance comparison of algorithms, the MMA which uses the high order statistics of transmitting signal has good performance in the MSE and SER compared to the SCA which is using the low order statistics. But in the recovered costellation and residual isi, the SCA has a good than the MMA.