Child malnutrition is pervasive in developing countries and anthropometric measures such as weight-for-height and height-for-age have proven reliable indicators of short term malnutrition and stunting. Rather than studying these indicators separately, we look at their interaction and carve out child health dynamics. Considering height-for-age a child's health stock and weight-for-lagged height a proxy for nutritional inputs, we develop a child health production function that features self-productivity of past health stocks and contemporaneous nutritional inputs. We test the model on a Senegalese panel of 271 children between 0 and 5 years employing dynamic panel methods to control for endogeneity in the production function. In line with previous evidence, we find that children can partially catch-up from malnutrition spells. Yet, child health stocks also deplete quickly and need constant updating in the form of nutrition. This demonstrates the importance of health memory and that malnutrition cannot be fought with snapshot interventions. Consequently, sustainable nutrition interventions have to be long term and yield higher returns the earlier they reach children.