The absorption spectra of the electronic S 1 √ S 0 transition of glyoxal molecules (C 2 H 2 O 2 ) embedded in He droplets (ഠ5500 atoms) show well-resolved vibronic bands with a width , 0.5 cm 21 . The phonon wings at higher frequencies have distinct gaps amounting to DE 8.1 K followed by a small maximum at 14.8 K. The phonon wing shape agrees with a theoretical simulation based on the dispersion curve of elementary excitations in bulk He II, providing the first evidence for superfluidity in the finite-sized He droplets. [S0031-9007(96)00383-3] PACS numbers: 67.40.Yv, 33.20.Kf, 67.40.Db A number of recent theoretical studies predict that 4 He clusters with more than about 64 atoms are superfluid with a transition temperature which is somewhat lower than the bulk l-point temperature T l 2.2 K [1-3]. So far, however, there is no direct experimental evidence for superfluidity in these nanosize liquid particles. Recently it has been possible to observe a very sharp rovibrational spectrum of single SF 6 molecules located in the interior of He droplets ͑N . 1000 atoms͒ which were produced in free jet expansions [4,5]. From this the rotational temperature was found to be T 0.37 6 0.05 K [5] in good agreement with theoretical predictions [6]. In addition, infrared spectra of SF 6 dimers indicate that these larger entities can also rotate freely in the He droplets [7].In the bulk the most direct evidence for superfluidity comes from neutron diffraction experiments which indicate sharp elementary excitations with a dispersion characterized by a maximum at E max 13.7 K ͑Q max 1.10 Å 21 ͒ called a maxon and the well known roton minimum at E rot 8.65 K ͑Q rot 1.91 Å 21 ͒ [8]. As first pointed out by Landau the sharp excitations at the roton minimum enable the fluid to flow unhindered at velocities below about 58 m͞s which is the most prominent manifestation of superfluidity. This critical velocity could so far only be observed for negative ions which were found to move without friction in liquid helium at P 25 atm and T 0.4 K [9]. Two-phonon Raman spectroscopy in bulk helium also has been shown to provide information on the elementary excitations [10]. In the quest for more direct spectroscopic probes of superfluidity several groups have developed sophisticated techniques to levitate atoms in liquid helium [11][12][13][14]. Up to now only broad lines of several cm 21 width could be observed. A recent study of the electronic spectra of Na 2 attached to the surface of He droplets reveals vibronic bands consisting of a sharp zero phonon line (ZPL) and an intense broad phonon wing (PW) [15]. In this system multiphonon processes appear to dominate the spectra and conceal the elementary excitations of the droplet.To circumvent these difficulties we have undertaken the first spectroscopic experiments with a simple organic molecule. Glyoxal (C 2 H 2 O 2 ) was chosen since its visible spectroscopy has been studied both as a free molecule and in cryomatrices [16,17]. Compared to the alkali metals glyoxal is readily solvated by helium...