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In this paper, we study cross-layer design for congestion control in multihop wireless networks. In previous work, we have developed an optimal cross-layer congestion control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal cross-layer congestion control scheme has to solve a complex global optimization problem at each time, and is hence too computationally expensive for online implementation. In this paper, we study how the performance of cross-layer congestion control will be impacted if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study both the case when the number of users in the system is fixed and the case with dynamic arrivals and departures of the users, and we establish performance bounds of cross-layer congestion control with imperfect scheduling. Compared with a layered approach that does not design congestion control and scheduling together, our cross-layer approach has provably better performance bounds,and substantially outperforms the layered approach. The insights drawn from our analyzes also enable us to design a fully distributed cross-layer congestion control and scheduling algorithm for a restrictive interference model.