This volume collects the results of a workshop held at Aachen, West-Germany, Oct. 12 - Oct. 14, 1981. The purpose in bringing together scientists actively working in the field of numerical methods in flame propagation was two-fold: 1. To confront them with recent results obtained by large ac- tivation-energy asymptotics and to check these numerically. 2. To compare different numerical codes and different trans- port models for flat flame calculations...