The theories of continuum mechanics and molecular physics are brought together to provide constitutive relations for dilute polymer solutions. The required compatibility shows that the stress tensor is composed of a sum of stress tensors, each satisfying Oldroyd's differential constitutive equation. In each equation, the higher order strain rate terms are not retained, and the five material constants are found solely by utilizing results from Rouse's molecular theory. When the fluid acceleration is small, it is shown that the set of constitutive relations may be approximated by a single equation of the Oldroyd type, containing only two material constants.