  A theoretical study of the magnetoelectronic properties of zigzag and
armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive
Green's function method, we study the band structure of BGNs in uniform
perpendicular magnetic fields and discuss the zero-temperature conductance for
the corresponding clean systems. The conductance quantized as 2(n+1)G_ for the
zigzag edges and nG_0 for the armchair edges with G_{0}=2e^2/h being the
conductance unit and $n$ an integer. Special attention is paid to the effects
of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a
small degree of edge disorder is already sufficient to induce a transport gap
around the neutrality point. We further perform comparative studies of the
transport gap E_g and the localization length in bilayer and monolayer
nanoribbons. While for the GNRs E_{g}^{GNR}is proportional to 1/W, the
corresponding transport gap E_{g}^{BGN} for the bilayer ribbons shows a more
rapid decrease as the ribbon width W is increased. We also demonstrate that the
evolution of localization lengths with the Fermi energy shows two distinct
regimes. Inside the transport gap, xi is essentially independent on energy and
the states in the BGNs are significantly less localized than those in the
corresponding GNRs. Outside the transport gap \xi grows rapidly as the Fermi
energy increases and becomes very similar for BGNs and GNRs.
