Parallel interference cancellation (PIC) is considered a simple yet effective multiuser detector for direct-sequence code-division multiple-access (DS-CDMA) systems. However, its performance may deteriorate due to unreliable interference cancellation in the early stages. Thus, a partial PIC detector, in which partial cancellation factors (PCFs) are introduced to control the interference cancellation level, has been developed as a remedy. Recently, an interesting adaptive multistage PIC algorithm was proposed. In this scheme, coefficients combining the channel responses and optimal PCFs are blindly trained with the least mean square (LMS) algorithm. The algorithm is simple to implement, inherently applicable to time-varying environments, and superior to the non-adaptive type of partial PICs. Despite its various advantages, its performance has not been theoretically analyzed yet. The contribution of this paper is to fill the gap by analyzing an adaptive two-stage PIC in AWGN channels. We explicitly derive the analytical results for optimal weights, weight-error means, and weight-error variances. Based on these results, we finally derive the output bit error rate (BER) for each user. Simulation results indicate that our analytical results highly agree with empirical ones.