This paper tackles online scheduling of electric vehicles (EVs) in an adaptive charging network (ACN) with local and global peak constraints. Given the aggregate charging demand of the EVs and the peak constraints of the ACN, it might be infeasible to fully charge all the EVs according to their charging demand. Two alternatives in such resource-limited scenarios are to maximize the social welfare by partially charging the EVs (fractional model) or selecting a subset of EVs and fully charge them (integral model). The critical challenge is the need for online solution design since in practical scenarios the scheduler has no information of future arrivals of EVs in a timecoupled underlying problem. For the fractional model, we devise both offline and online algorithms. We prove that the offline algorithm is optimal. Using competitive ratio as the performance measure, we prove the online algorithm achieves a competitive ratio of 2. The integral model, however, is more challenging since the underlying problem is NP-hard due to 0/1 selection criteria of EVs.We devise a low-complexity primal-dual scheduling algorithm that achieves a bounded approximation ratio. Built upon the offline approximate algorithm, we propose an online algorithm and analyze its competitive ratio in special cases.