Using coalgebraic methods, we extend Conway's original theory 
of games to include infinite games (hypergames). We take the view 
that a play which goes on forever is a draw, and hence rather than 
focussing on winning strategies, we focus on non-losing strategies. Infinite 
games are a fruitful metaphor for non-terminating processes, Conway's 
sum of games being similar to shuffling. Hypergames have a rather 
interesting theory, already in the case of generalized Nim. The theory of 
hypergames generalizes Conway's theory rather smoothly, but significantly. 
We indicate a number of intriguing directions for future work. 
We briefly compare infinite games with other notions of games used in 
computer science.