We investigate the Hamiltonian dynamics of two low-dimensional quantum spin systems in a random ÿeld, at the inÿnite-temperature limit: the XY chain and the two-leg XY ladder with interchain Ising interactions. We determine the longitudinal spin autocorrelation functions of the spin-1 2 XY chain and ladder in the presence of disordered ÿelds by using the method of recurrence relations. The ÿrst six basis vectors for the chain and the ÿrst four basis vectors for the ladder of the dynamic Hilbert spaces of z j (t), as well as the corresponding recurrents and moments of the time-dependent autocorrelation function, are analytically computed for bimodal distributions of the ÿelds. We did ÿnd a remarkable result in the disordered models. Cases with a fraction of p sites under ÿeld BB and a fraction of 1 -p sites under the ÿeld BA have the same longitudinal dynamics as those with p sites under ÿeld BA and 1 -p sites under the ÿeld BB. We also ÿnd that both the XY chain and the two-leg XY ladder with Ising interchain coupling in the presence of random ÿelds are sensitive to the percentage of disorder but not to the intensity of the ÿelds.