This paper summarises the results of extensive research to determine the limit of safety against flame transmission for flame arrestors of relatively small size fitted with arrestor elements made of crimped metal ribbon. Depending on the reactivity of the fuel gas/air mixture and the tube geometry the running up to detonation and hence the stressing of a flame arrestor by a detonation is possible in longer tubes with relatively small diameters. Only with reactive gas phases of explosion group I this stressing case for a flame arrestor can be excluded. With detonative gas phases the stressing of the flame arrestor decisively depends on the place of installation with respect to the point of transition from deflagration to detonation in the system considered. Five different stressing cases with a probably very different limiting pressure of safety against flame transmission must be distinguished. The results of the investigations will help to evaluate the results from testing of flame arrestors carried out according to the requirements in national and international standards or regulations.