Barker sequences have been used in many existing communications and ranging systems. Unfortunately, the longest known biphase and quadriphase Barker sequences are of lengths 13 and 15, respectively. In this paper, we introduce the so-called quasi-Barker sequences which achieve the minimum peak sidelobe level one within a certain window centered at the mainlobe. As our key results, all the best biphase and quadriphase quasi-Barker sequences of lengths up to 36 and 21, respectively, were obtained by an efficient computer search. These sequences may provide better multipath resistance and tracking accuracy in ranging applications.