This study investigates of-constructions in the predicates of two verbs, demonstrate and show, in academic discourse. A construction perspective is taken to examine how the two predicate constructions (‘demonstrate N1 of N2’ and ‘show N1 of N2’) would differ when the information-weighting of N1 and N2 are considered. The noun phrases were compared following Sinclair’s (1991) conception of semantic headedness. He notes the peculiarity of of through the expression of double-headed constructions (i.e., considering both N1 and N2 as the semantic heads). This study adopts this framework and applies it to analyze the of-constructions of the two synonymous verbs. The results show that headedness of the of-constructions can be used to identify the subtle differences between the two synonyms. Demonstrate displays greater information weight predominated by doubleheaded onstructions and tends to be associated with abstract conception. Show follows closely after demonstrate, but further analysis reveals that show tends to provide more ‘relational’ evidence described in terms of partitive uses through nouns like variety, degree, incidence, level, rate and range.