This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are considered. Results include new upper bounds, network error-correction coding strategies, and examples of network families where our bounds are tight. An example is provided of a network where the capacity is 50% greater than the best rate that can be achieved with linear coding. While coding at the source and sink suffices in networks with equal link capacities, in networks with unequal link capacities, it is shown that intermediate nodes may have to do coding, nonlinear error detection, or error correction in order to achieve the network error-correction capacity.