We prove two sufficient conditions for Hamiltonian cycles in balanced bipartite digraphs. Let D be a strongly connected balanced bipartite digraph of order 2a. Then: (i) If a≥4 andmax{d(x),d(y)}≥2a−1 for every pair of vertices {x,y} with a common out-neighbour, then either D is Hamiltonian or D is isomorphic to a certain digraph of order eight which we specify. (ii) Ifa≥4 andd(x)+d(y)≥4a−3 for every pair of vertices {x,y} with a common out-neighbour, then D is Hamiltonian. The first result improves a theorem of Wang and the second result, in particular, establishes a conjecture due to Bang-Jensen, Gutin and Li for strongly connected balanced bipartite digraphs of orders at least eight.