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We present IRAM Plateau de Bure Interferometer 3‐mm observations of  CO  J (1 → 0)  emission in two 24‐μm selected starburst galaxies in the outskirts  (∼2–3 R  virial )  of the rich cluster Cl 0024+16  ( z = 0.395) . The galaxies' inferred far‐infrared luminosities place them in the luminous infrared galaxy (LIRG) class  ( L  FIR  &gt; 10 11  L ⊙ ) , with star formation rates of  ∼60 M ⊙  yr −1  . Strong  CO  J (1 → 0)  emission is detected in both galaxies, and we use the CO line luminosity to estimate the mass of cold molecular gas,   M (H 2 ) . Assuming   M (H 2 )/ L ′ CO = 0.8 M ⊙  (K km −1  pc 2 ) −1  , we estimate   M (H 2 ) = (5.4–9.1) × 10 9  M ⊙   for the two galaxies. We estimate the galaxies' dynamical masses from their CO line widths,   M  dyn ∼ 1–3 × 10 10  M ⊙  , implying large cold gas fractions in the galaxies' central regions. At their current rates, they will complete the assembly of   M  ★ ∼ 10 10  M ⊙   and double their stellar mass within as little as ∼150 Myr. If these galaxies are destined to evolve into S0s, then the short time‐scale for stellar mass assembly implies that their major episode of bulge growth occurs while they are still in the cluster outskirts, long before they reach the core regions. Subsequent fading of the disc component relative to the stellar bulge after the gas reservoirs have been exhausted could complete the transformation of spiral‐to‐S0.

CO interferometry of gas‐rich spiral galaxies in the outskirts of an intermediate redshift cluster