A two step procedure for two-channel signal separation is developed. We are particularly interested in separating signals generated by two sources received by two sensors. In the first step, time delays of the interfering signals are estimated using the usual or Fractional Lower Order Statistic (FLOS) type cross correlation estimates. In the next stage, Least Mean Square (LMS) and Normalized Least Mean-p Norm (NLMP) algorithms are used to cancel interference terms from each channel. The selection of the algorithms are made by referring to the characteristics of the signals. In particular, FLOS type cross correlation estimates and the Normalized Least Mean-p Norm algorithms demonstrate robust performance in the presence of impulsive signals. Simulation results for Gaussian and a-stable signals are presented. The robust algorithms are also effective in separating speech signals.