This book constitutes the thoroughly refereed post-proceedings of the First Combined International Workshops on Formal Approaches to Software Testing, FATES 2006, and on Runtime Verification, RV 2006, held within the scope of FLoC 2006, the Federated Logic Conference in Seattle, WA, USA in August 2006. The 14 revised full papers presented together with 3 invited lectures were carefully selected from 31 initial submissions. The papers discuss formal approaches to test and analyze programs and monitor and guide their executions by using techniques from areas like theorem proving, model checking, constraint resolution, static program analysis, abstract interpretation, Markov chains, and various others. Formal approaches to runtime verification use formal techniques to improve traditional ad-hoc monitoring techniques used in testing, debugging, performance monitoring, fault protection, etc.