Our model for the process of gene assembly in ciliates is highly nondeterministic in the sense that for a given micronuclear gene there may exist many different strategies for assembling that gene using the three operations Id, hi, and dlad. For instance, using computer simulations, we noticed that there are 3,060 different sequential strategies to assemble the actin gene in Sterkiella nova,and 23,940 different sequential assembly strategies for the same gene in Sterkiella trifallax. For this reason, it is important to study the invariants of gene assembly, i.e., those properties of gene assembly that are common to all these strategies.