In networks which employ spread-spectrum signaling, capture and correct reception of one out of several packets transmitted to a common receiver by contending users is possible. For the case in which all the contending users employ the same spread-spectrum code, the probability of acquiring and retaining capture is evaluated via accurate approximations and tight bounds for direct-sequence, and frequency-hopped spread-spectrum signaling formats. From this probabilistic capture model, a (deterministic) threshold capture model is also derived. Both these models of capture are then incorporated into the binary tree collision resolution algorithm which takes advantage of the capture capability provided by the spread-spectrum signaling. Stable throughputs are evaluated for two types of feedback: (i) feedback with capture (4-ary), in which case the receiver can distinguish between capture and success slots (as well as between idle slots and collision slots as in the ternary feedback non-capture case), and (ii) feedback without capture (ternary) in which case the receiver can not distinguish between capture and success slots.