Decorrelating, LMMSE, and the noise-whitening multiuser detectors for code division multiple access (CDMA) are ideally infinite memory length (IIR) detectors. To obtain more practical and robust systems linear finite memory-length (FIR) multiuser detectors are studied. They are obtained by truncating the IIR detectors or by finding optimal FIR detectors. The optimal FIR detectors are shown to equal asymptotically the truncated detectors under mild conditions. The stable truncated decorrelating (or LMMSE) detector is shown to be near-far resistant, if the received powers are upper bounded, and if the memory-length is large enough (but finite). Numerical examples demonstrate that moderate memory-lengths are sufficient to obtain the performance of the IIR detectors even with severe near-far problem.