AbstractIn this paper, a colouring game and two versions of marking games (the weakand the strong) on digraphs are studied. We introduce the weak game chromaticnumber χwg(D) and the weak game colouring number wgcol(D) of digraphs D. It isproved that if D is an oriented planar graph, then χwg(D) 6 wgcol(D) 6 9, and if Dis an oriented outerplanar graph, then χwg(D) 6 wgcol(D) 6 4. Then we study thestrong game colouring number sgcol (D) (which was first introduced by Andres asgame colouring number) of digraphs D. It is proved that if D is an oriented planargraph, then sgcol (D) 6 16. The asymmetric versions of the colouring and markinggames of digraphs are also studied. Upper and lower bounds of related parametersfor various classes of digraphs are obtained...