In distributed radar systems, when several transmitters radiate simultaneously, the reflected signals need to be distinguished at the receivers to detect various targets. If the transmit signals are in different frequency bands, they require a large overall bandwidth. Instead, a set of pseudo-orthogonal waveforms derived from the Zadoff-Chu (ZC) sequences could be accommodated in the same band, enabling the efficient use of available bandwidth for better range resolution. In such a design, special care must be given to the 'near-far' problem, where a reflection could possibly become difficult to detect due to the presence of stronger reflections. In this work, a scheme to detect multiple targets in such distributed radar systems is proposed. It performs successive cancellations (SC) starting from the strong, detectable reflections in the domain of the Discrete Chirp-Fourier Transform (DCFT) after compensating for Doppler shifts, enabling the subsequent detections of weaker targets which are not trivially detectable. Numerical simulations corroborate the efficacy and usefulness of the proposed method in detecting weak target reflections.