Context : Submillimeter galaxies ( SMGs ) are distant , dusty galaxies undergoing star formation at prodigious rates .
Recently there has been major progress in understanding the nature of the bright SMGs ( i.e . S _ { 850 \mu m } > 5 mJy ) .
The samples for the fainter SMGs are small and are currently in a phase of being built up through identification studies .

Aims : We study the molecular gas content in two SMGs , SMMJ163555 and SMMJ163541 , at redshifts z = 1.034 and z = 3.187 with un-lensed submillimeter fluxes of 0.4 mJy and 6.0 mJy .
Both SMGs are gravitationally lensed by the foreground cluster Abell 2218 .

Methods : IRAM Plateau de Bure Interferometry observations at 3mm were obtained for the lines CO ( 2-1 ) for SMMJ163555 and CO ( 3-2 ) for SMMJ163541 .
Additionally we obtained CO ( 4-3 ) for the candidate z = 4.048 SMMJ163556 with an unlensed submm flux of 2.7 mJy .

Results : CO ( 2-1 ) was detected for SMMJ163555 at redshift 1.0313 with an integrated line intensity of 1.2 \pm 0.2 Jy km/s and a line width of 410 \pm 120 km/s .
From this a gas mass of 1.6 \times 10 ^ { 9 } M _ { \odot } is derived and a star formation efficiency of 440 L _ { \odot } /M _ { \odot } is estimated .
CO ( 3-2 ) was detected for SMMJ163541 at redshift 3.1824 , possibly with a second component at redshift 3.1883 , with an integrated line intensity of 1.0 \pm 0.1 Jy km/s and a line width of 280 \pm 50 km/s .
From this a gas mass of 2.2 \times 10 ^ { 10 } M _ { \odot } is derived and a star formation efficiency of 1000 L _ { \odot } /M _ { \odot } is estimated .
For SMMJ163556 the CO ( 4-3 ) is undetected within the redshift range 4.035 - 4.082 down to a sensitivity of 0.15 Jy km/s .

Conclusions : Our CO line observations confirm the optical redshifts for SMMJ163555 and SMMJ163541 .
The CO line luminosity L ^ { \prime } _ { CO } for both galaxies is consistent with the L _ { FIR } - L ^ { \prime } _ { CO } relation .
SMMJ163555 has the lowest far-infrared luminosity of all SMGs with a known redshift and is one of the few high redshift LIRGs whose properties can be estimated prior to ALMA .