A slotted asynchronous CDMA scheme controlling the time of arrival is proposed for distributed spread-spectrum packet radio networks where the transmission range is limited like an indoor wireless system. In this scheme, each terminal can send its packet randomly at any one of N w possible time instants, equally spaced over one period of direct-sequence spread-spectrum signals. Such transmissions initiated at different time instants can be resolved because of high time resolution of wideband signals if the channel delays associated with multipath are small due to limited transmission range. Quasi-synchronous distributed networks are considered to allow timing drift among terminals and reflect wireless multiple-access channels, in which C-T and R-T spreading code assignments are adopted to permit a contention mode only for the header portion. Throughput is evaluated under the spread ALOHA assumption on collision and also by reflecting the effect of the MAI in the header detection. Theoretical results show that the combination of the slotted asynchronous scheme with C-T assignment results in more significant improvement than the case of R-T assignment, and also the former provides the benefit of the efficient usage of spreading codes in a code-limited environment.