We study the Cauchy problem for the generalized Benjamin-Ono equation ∂ t u − D | D| 2 μ u = DV'( u), (∗) where D = d dx , U > 0 , and V ϵ E 1( R,R ) with V(0) = V′(0) = 0. Using commutator identities and estimates, we prove that the equation (∗) exhibits smoothing properties similar to those of the generalized Korteweg-de Vries equation (GKdV), which is the special case μ = 1 of (∗). If V satisfies suitable estimates at zero and at infinity, we prove that the Cauchy problem for the equation (∗) with initial data u(0) = u 0 has a solution u ϵ L ∞( R , l 2)∪ L 2 loc( R , H μ loc) if u 0 ϵ L 2, and has a solution u ϵ L ∞( R , H μ)∪ L 2 loc( R , H 2μ loc)if u 0 ϵ H μ (finite energy solution). In addition, we prove that the usual Benjamin-Ono equation ( μ = 1 2 , V′(u) = u 2 ) has a solution u ϵ L ∞( R , H 1)∪ L 2 loc( R , H 3 2 loc) for u 0 ϵ H 1. Those results are easily extended to related equations such as the intermediate long wave equation or the Smith equation.