  The possibility to explain the baryon asymmetry in the Universe through the
leptogenesis mechanism in the context of Adjoint SU(5) is investigated. In this
model the neutrino masses are generated through the Type I and Type III seesaw
mechanisms, and the field responsible for the Type III seesaw, called rho_3,
generates the B-L asymmetry needed to satisfy the observed value of the baryon
asymmetry in the Universe. We find that the CP asymmetry originates only from
the vertex correction, since the self-energy contribution is not present. When
neutrino masses have a normal hierarchy, successful leptogenesis is possible
for 10^{11} GeV < M_{\rho_3}^{NH} < 4 10^{14} GeV. When the neutrino hierarchy
is inverted, the allowed mass range changes to 2 10^{11} GeV < M_{\rho_3}^{IH}
< 5 10^{11} GeV. These constraints make possible to rule out a large part of
the parameter space in the theory which was allowed by the unification of gauge
interactions and the constraints coming from proton decay.
