In Argentina, bovine leukaemia virus (BLV) infection is common in dairy herds. The country currently has a National Voluntary Control Programme but relatively few farms have enrolled. However, there is increased interest from authorities and farmers to implement regional compulsory programmes but there is scarce quantitative information of the transmission of BLV in cattle herds. This information is a prerequisite to develop effective BLV control strategies. Mathematical modelling offers ways of integrating population-level knowledge and epidemiological data to predict the outcomes of intervention scenarios. The purpose of the current paper is to gain understanding about the dynamics of the transmission of BLV in dairy herds from Argentina by simulation and to compare various BLV transmission models and select the one that is most appropriate. The hypothetical herd is conceptually described in terms of BLV status as a population of individuals that are protected by maternal antibodies (M), that are susceptible (S), that are in the latent period (E) or that are infectious (I). BLV is spread by horizontal and vertical transmission. We used an age-structured population model and within-herd transmission was simulated by Monte Carlo techniques. The next-generation approach has been used for the systematic computation of the basic reproduction ratio (R0). Parameter values for disease transmission were derived from previously published data; rates of entry, exit or transition between age groups were calculated based on our previous study, observational data, expert opinions and literature. With these parameter values the probability of a minor outbreak was estimated to be 10%, the probability of extinction was estimated as <0.001% and the expected time to extinction as more than 80 years. The probability of a minor outbreak and changes in prevalence were different when the index case was an adult cow compared to introduction by a heifer. Prediction of prevalences from MSI models fit the data satisfactorily. R0 was estimated as 9.5. The sensitivity analysis on R0 showed that all measures directed to reduce the transmission rate are potentially effective given operational control measures. An important prediction of these models is that, even in a relatively small, closed dairy herd, the time-scale for a BLV outbreak may be as long as several years and within-herd control of BLV requires intensive efforts.