Competition from neighbouring trees generally has a negative effect on the growth of an individual tree; however, the magnitude of competition is expected to vary with size and proximity of the tree and its competitors. Eucalypt forests (natural/plantation) are widespread throughout the world, and have high economic, ecological and conservation importance. Recent work carried out in eucalypt forest of Western Australia showed that growth of individual trees could be explained by a flexible novel competition index that accounts for proximity and size of competitors. This study aimed to further test and extend those methods, by applying them to long-term time-series data on thinned and unthinned plots of two important new species (karri and marri) in a more productive environment. More specifically, we aimed to compare the usefulness of different competition indices (CIs) including a novel index using crown-width; develop models to understand and predict the growth of karri and marri individuals, using tree size and age; test whether including measures of neighbourhood competition would improve growth predictions for these species; validate the predictive ability of the models and analyse the sensitivity of their parameters; and investigate how many neighbouring trees or what neighbourhood distance needed to be considered when accounting for competition. Our new crown-width CI was useful, but not as useful as previous diameter-based CI. Diameter and age were significant predictors, and prediction was further improved by inter-tree competition. Leave-one-out cross-validation showed that our models are well validated, and sensitivity of karri model parameters was<13% while sensitivity of marri model parameters was a little higher (<20%). Including up to 14 competitors or competitors within ~7 m distance from the base of the target tree was optimal in predicting growth. Our new models and methods may help to identify trees to be removed during thinning and assist in determining the appropriate size of plots for studying the effect of competition on individual tree growth. New insights from this study include the individual tree growth models for karri and marri; validation and sensitivity analysis of these models; improved understanding of competition for two important new eucalypt species; a new crown and distance-based CI; and evidence for the usefulness of our recently developed diameter and distance-based CI for two new species.