We carry out a systematic investigation of the deenability of linear order on classes of nite rigid structures. We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in nite model theory, such as least xpoint logic LFP, partial xpoint logic PFP, innnitary logic L ! 1! with a nite number of variables, as well as the closures of these logics under implicit deenitions. Moreover, we show that the upper and lower bounds established here can not be made substantially tighter, unless outstanding conjectures in complexity theory are resolved at the same time.