In　this　paper,　a　colouring　game　and　two　versions　of　marking　games　(the　weak　and　the　strong)　on　digraphs　are　studied.　We　introduce　the　weak　game　chromatic　number　χwg(D)　and　the　weak　game　colouring　number　wgcol(D)　of　digraphs　D.　It　is　proved　that　if　D　is　an　oriented　planar　graph,　then　χwg(D)　≤　wgcol(D)　≤　9,　and　if　D　is　an　oriented　outerplanar　graph,　then　χwg(D)　≤　wgcol(D)　≤　4.　Then　we　study　the　strong　game　colouring　number　sgcol　(D)　(which　was　first　introduced　by　Andres　as　game　colouring　number)　of　digraphs　D.　It　is　proved　that　if　D　is　an　oriented　planar　graph,　then　sgcol　(D)　≤　16.　The　asymmetric　versions　of　the　colouring　and　marking　games　of　digraphs　are　also　studied.　Upper　and　lower　bounds　of　related　parameters　for　various　classes　of　digraphs　are　obtained.