This article is concerned with asynchronous consensus problems of continuous-time second-order agents with fixed topology and time-varying delays. It is assumed that each agent obtains the measurements of its states relative to its neighbours only at discrete times and the discrete times of each agent are independent of the others'. It is proven that the asynchronous consensus is equivalent to the global asymptotic stability of a time-varying discrete-time system with delays. Furthermore, a sufficient condition for asynchronous consensus is established in virtue of the Lyapunov's direct method. Simulations are performed to validate the theoretical results.