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We present a study of the charmless semileptonic B-meson decays B+ -> omegal+ nu and B+ -> eta l+ nu. The analysis is based on 383 million BBbar pairsrecorded at the Upsilon(4S) resonance with the BABAR detector. The omega mesonsare reconstructed in the channel omega -> pi+ pi- pi0 and the eta mesons in thechannels eta -> pi+ pi- pi0 and eta -> gamma gamma. We measure the branchingfractions B(B+ -> omega l+ nu) = (1.14 +- 0.16 (stat) +- 0.08 (syst)) x 10^-4and B(B+ -> eta l+ nu) = (0.31 +- 0.06 (stat) +- 0.08 (syst)) x 10^-4.

Measurement of the B+ -> omega l+ nu and B+ -> eta l+ nu Branching Fractions