This paper develops a model of foreign assistance where untied aid generates goodwill for a donor in a recipient country, thereby enhancing exports of the donor. Using an intertemporal maximizing model, we identify the optimal adjustment paths for tied and untied aid and the parameters upon which they depend. Estimates of these parameters are obtained from data on aid from seventeen OECD countries over the period 1972-1990. Results suggest that donor countries maintain a constant flow of untied aid in order to continually replenish the stock of goodwill, while adjusting the flow of tied aid over time.