This technical note proposes a general class of nonlinear protocols in the form of continuous state feedbacks for finite-time consensus in networks of integrator-like dynamic agents with directional link failure. These protocols, with adjustable terms, are applicable in a wide range of situations, such as with input saturation restrictions and with convergence rate constraints. Based on the assumption of a common positive dwell time for all active information links, it is shown that if the union of the interaction topology over some fixed length of time always contains a spanning tree, then the system will solve an asymptotical consensus problem; in addition, if the length sum of time intervals, over which the interaction topology contains a spanning tree, is larger than a threshold, determined by the state differences between agents, then the system will solve a finite-time consensus problem. The validity of the protocols is proven in the case with external reference inputs. Finally, simulations are presented to demonstrate the effectiveness of the theoretical results.