The parameter estimation problem in identifying the linear time invariant difference equation model of systems has been considered by different investigators from the point of view of correlation analysis. Their methods are in ‘ two steps ’ which first establish a weighting sequence model and then estimate the difference equation parameters. In this paper two algorithms based on correlation analysis are presented that directly estimate the difference equation parameters of linear SISO systems and do not need the intermediate step of determining the weighting sequence. Results of computer simulated examples are presented, comparing them with other existing algorithms and indicating the superiority of the new algorithms.