1.One of the major problems in understanding growth trends in long-lived trees is the difficulty of separately quantifying the effects of tree size and age. Careful statistical control of the axiomatic age×size covariation is therefore required to identify long-term trends in tree growth and their drivers, and to predict forests’ responses to environmental changes reliably. 2.To address this issue, we present a novel tree growth model: a ‘two-dimensional lognormal growth model’. This is an extension of the one-dimensional lognormal growth model, in which tree growth is modelled primarily as a function of size. Our model assesses the trend in tree growth over time by explicitly partitioning the effects of age and size, controlling the covariation. The model is then extended to incorporate the effects of neighbourhood crowding and individual tree variation. 3.To demonstrate our model, we apply it to long-term monitoring data from a mature (104-year- old) plantation of Japanese cedar. Thinning operations of various intensities have been applied to this plantation, and the diameter of each individual tree has been measured repeatedly. 4.We observed a pronounced age-related decline in diameter growth. However, at each age, greater tree size was associated with a higher growth rate. The growth-size curve predicted from the model became flatter with tree age, and the curve's peak shifted rightwards as tree age increased. The model reveals that the sensitivity of a target tree to neighbourhood crowding depends strongly on neighbours’ size, and also provides an estimate of among-tree variation in growth performance. 5.Although the relationships between growth, size and age in long-lived trees are very complex, our growth model supports the conclusion that it is possible to predict long-term trends in tree growth reliably with respect to both age and size. In addition, the model's flexibility will facilitate more robust testing of species-specific responses to long-term environmental changes.