The conditions for accurately intercepting hypersonic vehicles by low-speed interceptors in the terminal guidance process are examined, considering the general form of a guidance scheme. First, based on the concept of the engagement geometry, three interception scenarios are established considering different manoeuvring configurations of the interceptors and hypersonic vehicle. Second, the boundary conditions for intercepting hypersonic vehicles (with speeds higher than those of the interceptors) are specified for the three scenarios, considering several factors: the speed, path angle, line-of-sight angle, and available overload of the interceptor; path angle and manoeuvrability of the hypersonic vehicle; and relative distance between the interceptor and vehicle. A series of simulations are performed to clarify the influence of each factor on the interception performance in the three interception scenarios. The challenges associated with accurately intercepting hypersonic vehicles by low-speed interceptors are summarised, and several recommendations for designing guidance laws are presented.