Artificial immune systems can be applied to a variety of very different tasks including function optimization. There are even artificial immune systems tailored specifically for this task. In spite of their successful application there is little knowledge and hardly any theoretical investigation about how and why they perform well. Here rigorous analyses for a specific class of mutation operators introduced for function optimization called somatic contiguous hypermutation is presented. Different concrete instantiations of this operator are considered and shown to behave quite differently in general. While there are serious limitations to the performance of this type of operator even for simple optimization tasks it is proven that for some types of optimization problems it performs much better than standard bit mutations most often used in evolutionary algorithms. (C) 2010 Elsevier B.V. All rights reserved.