Mobile-edge computing (MEC) has recently emerged as a promising paradigm to liberate mobile devices from increasingly intensive computation workloads, as well as to improve the quality of computation experience. In this paper, we investigate the tradeoff between two critical but conflicting objectives in multi-user MEC systems, namely, the power consumption of mobile devices and the execution delay of computation tasks. A power consumption minimization problem with task buffer stability constraints is formulated to investigate the tradeoff, and an online algorithm that decides the local execution and computation offloading policy is developed based on Lyapunov optimization. Specifically, at each time slot, the optimal frequencies of the local CPUs are obtained in closed forms, while the optimal transmit power and bandwidth allocation for computation offloading are determined with the Gauss-Seidel method. Performance analysis is conducted for the proposed algorithm, which indicates that the power consumption and execution delay obeys an [O(1/V),O(V)] tradeoff with V as a control parameter. Simulation results are provided to validate the theoretical analysis and demonstrate the impacts of various parameters to the system performance.