In this paper, we answer the question about the existence of the minimal speed of front propagation in a delayed version of the Murray model of the Belousov-Zhabotinsky (BZ) chemical reaction. It is assumed that the key parameter r of this model satisfies 0 < r <= 1 that makes it formally monostable. By proving that the set of all admissible speeds of propagation has the form [c(*), +infinity), we show here that the BZ system with r is an element of (0, 1] is actually of the monostable type (in general, c(*) is not linearly determined). We also establish the monotonicity of wavefronts and present the principal terms of their asymptotic expansions at infinity (in the critical case r = 1 inclusive).