The paper is concerned with the limit design of statically indeterminate beams or frames under the action of given loads. The limit moments· under which individual sections act as yield hinges are supposed to be known throughout the structure and the safety factor against collapse is sought. This safety factor is defined as. the multiple to which the actual loads must be increased before yield. hinges develop in a number sufficient to render the structure unstable. Two extremum principles are established for the safety factor. With these principles two estimates of the safety factor can, be obtained, one of which is known to be too small whereas the other is known to be too large. The gap between these estimates can be reduced by a repeated application of the extremum principles.