Spectra of NeC2D4 and ArC2D4 are studied in the ¦Í11 fundamental band region of C2D4 (¡Ö2200 cm?1) using a tuneable quantum cascade laser to probe a pulsed supersonic slit jet expansion. The spectra are those of perpendicular bands of near-prolate asymmetric rotors, but with a doubling of transitions due to tunneling. These tunneling splittings are due to hindered internal rotation of C2D4 around its CC axis, and are more prominent for NeC2D4 than for ArC2D4. The analysis yields the first direct measurement of the A rotational constants for these complexes, and shows that the vibrational shifts are very small (<0.3 cm?1). Attempts to observe the spectrum of HeC2D4 were not successful.