We consider the effect of the presence of molecular hydrogen on plasma recombination at temperatures of a few electron volts. The r$\hat{o}$le of 2-body processes such as ion conversion and dissociative attachment in accelerating the recombination is exposed, both in a simplified model, which can be solved analytically, and in more realistic numerical calculations. All the important atomic and molecular processes are included in a set of non-linear rate equations, from which we identify the important parameters of the model and thereby show which cross sections are critical. Although we do not include transport explicitly we are able to extend the model to mimic recycling at the plasma edge. This enables us to demonstrate the importance of the contribution of H$_{2}$ to recombination. Our model is primitive, but it enables us to identify processes which are important in modelling H$_{2}$-plasma interactions, and which will therefore have to be treated in more complex plasma codes. We find that some of the ideas basic to atomic modelling of plasmas may have to be revised if molecular processes are important in the plasma dynamics. In particular, the non-linearities we discuss lead to instabilities, which allow the co-existence of several solutions for the same physical parameters.