We present an overview of our ongoing work on parallelizing self-adjusting-computation techniques. In self-adjusting computation, programs can respond to changes to their data (e.g., inputs, outcomes of comparisons) automatically by running a change-propagation algorithm. This ability is important in applications where inputs change slowly over time. All previously proposed self-adjusting computation techniques assume a sequential execution model. We describe techniques for writing parallel self-adjusting programs and a change propagation algorithm that can update computations in parallel. We describe a prototype implementation and present preliminary experimental results.