Maneuvering target tracking is an important problem in radar data processing. Several algorithms such as Singer，IE，VD，and IMM algorithms have been studied in the last few years and have been summerized in this paper. The real time constrains have to be considered in application. This paper presents a modified input estimstion (MIE) algorithm and an adaptive α-β algorithm. Both algorithms require a minimum amount of computation. Computer simulation studies have shown the effectiveness of the two algorithms in tracking maneuvering targets.