The technique of relative-flow analysis on isentropic surfaces is used to examine the large- (“synoptic”-) scale situations associated with selected severe local storms near southern England and over the mid-western U.S.A. (including the Horsham, Wokingham, and Geary storms whose behaviour has been described in several previous publications). The storms occur ahead of major troughs, in the vicinity of confluence-lines (usually recognised as cold fronts over western Europe but as “dry-lines” over the U.S.A.), where an increase of wind with height favours the organisation and intensification of cumulonimbus convection. Extreme instability arises where small-scale convection is confined to a lowermost 1 or 2 km (leading to an abnormally high wetbulb potential temperature) beneath a plume of very warm air lying downwind of an extensive arid plateau (Spain or Mexico). The instability is released where the (backed) low-level flow eventually reaches the edge of the restraining plume aloft. It appears that the occurrence of severe local storms demands a peculiarly favourable combination of geographical features and atmospheric flow-pattern.