Eenergy transfer in the B800 ring of the LH2 antenna of the purple bacteria Rhodopseudomonas (Rps.) acidophila and Rhodospirillum (Rs.) molischianum was studied at room temperature using three-pulse echo peak shift (3PEPS) and transient grating (TG) techniques. From the transient grating experiments, we found the B800 --> B850 energy transfer rates to be 600-700 fs for both species. The anisotropy of the TG signal decays in about 1 ps for both species, which is ascribed to B800 --> B800 energy transfer. The occurrence of B800 --> B800 energy transfer was further substantiated by 3PEPS experiments. When measured over the whole B800 band, the initial peak shift of about 30 fs exhibited a fast < 100 fs decay to about 10 fs due to the coupling to protein phonons, followed by a slow phase of about I ps, during which the peak shift decayed to 1-3 fs, Polarized 3PEPS experiments systematically resulted in smaller peak shift values for the third pulse polarized perpendicular to the first two than for the third pulse parallel to the first two. Furthermore, frequency-resolved 3PEPS experiments performed on LH2 of Rs. molischianum showed a large difference in peak shift decay rates when tuning over the B800 band. The "blue" peak shifts did not decay after the initial sub-100 fs phase, while "red" peak shifts decayed much faster than the whole band signal. All these observations confirm the presence of B800 --> B800 energy transfer. Simulations using the Brownian oscillator model allowed the determination of an equilibration rate of 1100 fs for Rps. acidophila and 800 fs for Rs. molischianum. For a model in which the spectral equilibration in a ring occurs by single hopping steps between adjacent pigment molecules, these times correspond to 2.2 ps (Rps. acidophila) and 1.6 ps (Rs. molischianum) for a single step. Strong oscillations with a predominant frequency of 162 cm(-1) are observed in the peak shift decays of both species.