The essential oil compositions of the rhizomes of Cyperus conglomeratus (Cyperaceae) collected from Oman and the leaves of two Annonaceae plants, Desmos chinensis var. lawii and Cyathocalyx zeylanicus collected from India were studied by GC, GC-MS and 13C NMR spectroscopy. Twenty-six compounds, representing 84.4% of the oil were identified in C. conglomeratus, where eugenol (31.3%), α-cyperone (10.5%) and cyperotundone (8.4%) were the major compounds. Twelve compounds, constituting 100%, were identified in D. lawii oil, of which benzyl benzoate (58.7%), β-caryophyllene (23.2%), limonene (4.9%) and α-humulene (4.0%) were the major constituents. Thirty-two compounds, comprising 98.0%, were identified in C. zeylanicus oil, of which β-caryophyllene (21.6%), α-pinene (20.4%) and E-β-ocimene (11.8%) were the major components. The antibacterial and antifungal activities of the oils were tested against a panel of five bacterial and two fungal strains. The oils showed moderate activity against all the tested microbial strains. The minimum inhibitory concentrations of the oils were also determined.