A decentralized dynamic event-triggered tracking control problem is investigated for a class of p-normal interconnected time-delay nonlinear systems with asymmetric constraints. First, a new event-triggered mechanism (ETM) is constructed by designing a dynamic variable law, which effectively reduces the number of controller updates. The introduced constants provide an obvious solution for the proof of Zeno phenomenon. Second, a barrier Lyapunov function (BLF) is constructed with the help of sign functions to achieve time-varying asymmetric constraints. Meanwhile, we improve the previous neural networks (NNs) approximation scheme and dynamic gain technique in order to handle unknown interconnection functions and time-delay signals, respectively. Then, it is rigorously proved that all signals in the system are bounded, and the error signals are constrained within the time-varying asymmetric bounds. Finally, the feasibility of the scheme is verified by simulation examples.