Partial parallel-interference-cancelation (PIC) is a well-known multiuser detection technique for DS/CMDA systems. Conventionally, partial-cancelation- factors (PCFs) are optimally derived and kept constant in a designated interval. Recently, a special kind of partial PIC was proposed. In the approach, PCFs are adaptively trained (chip-by-chip) using the least-mean-square (LMS) algorithm, and PCFs are updated with a bit-by-bit fashion. It has been shown that the adaptive partial PIC detector outperforms conventional partial PIC. Despite its good performance, performance analysis of the approach has not been explored yet. This paper is aimed to fill the gap by conducting the performance analysis of an adaptive two-stage partial PIC detector. We first analyze optimal weights (i.e., PCFs), weight error means, and weight error variances. Simulation results indicates that our analytical results highly agree with empirical ones.