Recent theoretical studies with alkali atoms A * excited to high Rydberg states predicted the existence of ultra long-range molecular bound states. Such excited dimers have large electric dipole moments which, in combination with their long radiative lifetimes, make them excellent candidates for manipulation in applications. This letter reports on experimental investigations of the selfbroadening of Rb principal series lines, which revealed multiple satellites in the line wings. The positions of the satellites agree quantitatively with theoretically-predicted minima in the excited long-range Rydberg states of Rb2.PACS numbers: 32.80. Rm, 32.80.Pj, 34.20.Cf Two different types of bound Rydberg molecules have been proposed in recent years as intriguing candidates for possible study. In the first case [1,2,3,4,5], a bound state is created by the interaction between an excited atom (A * ) and a ground state atom (A). The properties of low-energy scattering of the quasi-free electron of the Rydberg atom A * on the perturber A create the attraction needed for dimer formation. These Rydberg molecules are comparable to the size of the excited atoms, and the corresponding electronic wave functions are characterized by specific spatial forms, two of which are the "trilobite" and "butterfly" states. These molecules are also predicted to be polar diatomic molecules possessing dipole moments (even the homonuclear species) that are huge compared to typical polar diatomic molecules. This property makes them easy to manipulate by even very small fields. A growing body of theoretical evidence strongly suggests the existence of these unusual molecular states, whose Born-Oppenheimer potential curves oscillate like a wavefunction (see, e.g., Refs. [6,7,8,9, 10]) But until now, their existence has not been confirmed experimentally.The second type of bound molecular Rydberg state is predicted to be created by the interaction of two Rydberg atoms A * + A * at very large distances R [11]. Here, the potential energy curve can be exclusively described by the long-range electrostatic interaction as a sum of C n /R n terms. The binding energies of both types of proposed long-range Rydberg molecules are very small in comparison with thermal kinetic energies at room temperatures. However, their formation and detection was predicted to be possible in ultra-cold gases or BoseEinstein condensates. Laser spectroscopic experiments performed in ultra-cold gases ([12, 13, 14] and references therein) have provided evidence for the existence of bound molecular Rydberg states of the A * +A * type [12,14].Our letter is focused on the experimental verification of the oscillatory bound state potentials in the Rb * +Rb system associated with electron-atom scattering resonances. In contrast to experiments mentioned above, we apply the well-established method of spectral line wing absorption measurement under thermal conditions [15]. Such measurements reveal satellites in the wings of collisionally-broadened lines at extrema in difference potentials of ...