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In this paper, we study cross-layer design for rate control in multihop wireless networks. In our previous work, we have developed an optimal cross-layered rate 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-layered rate control scheme has to solve a complex global optimization problem at each time, and hence is too computationally expensive for online implementation. In this paper, we study how the performance of cross-layer rate control can 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 desirable results on the performance bounds of cross-layered rate control with imperfect scheduling. Compared with a layered approach that does not design rate control and scheduling together, our cross-layered approach has provably better performance bounds, and substantially outperforms the layered approach. The insights drawn from our analyses also enable us to design a fully distributed cross-layered rate control and scheduling algorithm for a restrictive interference model.