Time delay is a phenomenon which is common in signal processing, communication, control applications, etc. The special feature of time delay that makes it attractive is that it is a commonly faced problem in many systems. A literature search on time-delay identification highlights the fact that most studies focused on numerical solutions. In this study, a novel online adaptive time-delay identification technique is proposed. This technique is based on an adaptive update law through a minimum-maximum strategy which is firstly applied to time-delay identification. In the design of the adaptive identification law, Lyapunov-based stability analysis techniques are utilised. Several numerical simulations were conducted with Matlab/Simulink to evaluate the performance of the proposed technique. It is numerically demonstrated that the proposed technique works efficiently in identifying both constant and disturbed time delays, and is also robust to measurement noise.