Plants respond to nitrogen availability by changing their root : shoot ratios. One hypothesis used to explain this allocation is that plants optimize their behaviour by maximizing their relative growth rate. The consequences of this hypothesis were investigated by formulating two models for root : shoot allocation, with and without explicit inclusion of maintenance respiration. The models also took into account that relative growth rate is a linear function of plant nitrogen concentration. The model without respiration gave qualitatively reasonable results when predictions were compared with observed results from growth experiments with birch and tomato. The explicit inclusion of maintenance respiration improved considerably the agreement between prediction and observation, and for birch was within the experimental accuracy. Further improvements will require additional details in the description of respiratory processes and the nitrogen uptake function. Plants growing under extreme nutrient stress may also optimize their behaviour with respect to other variables in addition to relative growth rate.