This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the stability of these algorithms. It suggests that several existing algorithms might not be stable but prescribes a technique to make them stable. It also reports the results of experiments with local transductive regression demonstrating the benefit of our stability bounds for model selection, in particular for determining the radius of the local neighborhood used by the algorithm.