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Context: Submillimeter galaxies (SMGs) are distant, dusty galaxies undergoingstar formation at prodigious rates. Recently there has been major progress inunderstanding the nature of the bright SMGs (i.e. S(850um)>5mJy). The samplesfor the fainter SMGs are small and are currently in a phase of being built upthrough identification studies. Aims: We study the molecular gas content in twoSMGs, SMMJ163555 and SMMJ163541, at z=1.034 and z=3.187 with unlensed submmfluxes of 0.4mJy and 6.0mJy. Both SMGs are gravitationally lensed by theforeground cluster A2218. Methods: IRAM Plateau de Bure Interferometryobservations at 3mm were obtained for the lines CO(2-1) for SMMJ163555 andCO(3-2) for SMMJ163541. Additionally we obtained CO(4-3) for the candidatez=4.048 SMMJ163556 with an unlensed submm flux of 2.7mJy. Results: CO(2-1) wasdetected for SMMJ163555 at z=1.0313 with an integrated line intensity of1.2+-0.2Jy km/s and a line width of 410+-120 km/s. From this a gas mass of1.6x10^9 Msun is derived and a star formation efficiency of 440Lsun/Msun isestimated. CO(3-2) was detected for SMMJ163541 at z=3.1824, possibly with asecond component at z=3.1883, with an integrated line intensity of 1.0+-0.1 Jykm/s and a line width of 280+-50 km/s. From this a gas mass of 2.2x10^10 Msunis derived and a star formation efficiency of 1000 Lsun/Msun is estimated. ForSMMJ163556 the CO(4-3) is undetected within the redshift range 4.035-4.082 downto a sensitivity of 0.15 Jy km/s. Conclusions: Our CO line observations confirmthe optical redshifts for SMMJ163555 and SMMJ163541. The CO line luminosityL'_CO for both galaxies is consistent with the L_FIR-L'_CO relation. SMMJ163555has the lowest FIR luminosity of all SMGs with a known redshift and is one ofthe few high redshift LIRGs whose properties can be estimated prior to ALMA.

New CO detections of lensed submillimeter galaxies in A2218: Probing molecular gas in the LIRG regime at high redshift