The next-nearest-neighbour Ising model with competing nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions, provides an example of a system in which massless modes destroy order at any finite temperature. This occurs only at a critical ratio, Kc, of the nnn and nn interactions. In this paper we investigate the role of long relaxation times in determining the behaviour of the system when the ratio of the nnn and nn interactions, K, is at and close to this critical ratio. Despite the absence of an order–disorder transition in systems with K = Kc, in Monte Carlo simulations reported here the temperature-dependent behaviour of the relaxation times indicates the existence of a glass transition with a glass transition temperature of Tg ≈ 0.26 in a model with nn interaction J = kB = 1.