In the article “Geodetic games for graphs” by F. Buckley and F. Harary the geodetic game on a generalized wheel Wm,nis stated to be won by the first player iff m + n is odd. This is incorrect; in this paper we show that the necessary and sufficient condition for the first player is that (1) n ⋚ 4 and m + n is odd or m = 1 and n is even, (2) m = 2 and n = 5, (3) n < 5 and m ≥ 2 and either m or n is odd.