The probability of capture is evaluated for the situation in which several transmitters use the same spread-spectrum code to contend for the attention of a single receiver. The first stage in the capture mechanism is that of acquisition of capture; randomization of the arrival time has been proposed by Davis and Gronemayer to provide delay capture and the probability of this occurence has been derived. We are concerned with the second stage, that of retaining capture in the presence of interference from the contending users. The probability of retaining capture is computed via accurate approximations and upper bounds for direct-sequence, frequency-hopped and hybrid spread-spectrum signaling formats and for different data modulation and demodulation schemes. The calculation of the overall probability of capture is carried out for spread-spectrum systems with and without forward-error-control; in the latter case Reed-Solomon codes, as well as binary convolutional codes, are considered. Finally, the capability of rejecting primary multiple-access interference in spread-spectrum radio networks is examined by computing the maximum number of users which can contend for the same receiver without causing the probability of capture to fall below some desirable level.