Monte-Carlo simulations (MCS) and the path probability method (PPM) were used to study disorder→order transformations in bcc alloys having the AB3 stoichiometry. Both methods used an explicit vacancy mechanism of ordering and an activated-state rate theory for the vacancy jumps. We studied the evolution of short-range order (SRO) as well as B2 and D03 long-range order (LRO) in alloys that began as random solid solutions. The growth rates of SRO and LRO were significantly higher for the PPM than for the MCS. We attribute this difference to improper handling of correlated vacancy motions in the PPM. The PPM also suffered from an artificial incubation time for the initiation of LRO. Both the MCS and the PPM showed that SRO has a tendency to develop in two stages. In the first stage there is a quick relaxation of the SRO by itself. In the second stage, which occurs with a longer time constant, the SRO and LRO grow simultaneously. Parametric plots of one order parameter against another, here termed “kinetic paths”, are discussed. A variety of different kinetic paths through the B2 and D03 order parameters can be predicted theoretically, depending on the choice of interatomic potentials. This range of calculated kinetic paths is broad enough to encompass our experimental results of SRO and LRO evolution in Fe3Al.