The following has been posted on the Batman: Arkham Asylum boards relating to down loadable demos on the PS3 and 360 networks:

PLEASE! HELP! WILL THERE BE A DEMO FOR BATMAN: ARKHAM ASYLUM?

Is there a God? What is the meaning of life? Is there life on another planet? Why does Noel Edmonds still have a career? Some of humankind's greatest minds have wrestled with these age old questions for centuries. But one mystery, above all others, burdens humanity's collective conciousness...

Will there be a Batman: Arkham Asylum demo available for download and if yes what will it contain?

Friends, the answer is.... YES.

It gets better: the demo will be available for 360, PS3 and PC. Zing! However, we haven't announced when yet. We're planning to announce the date and content of the demo in the first half of July - if you want to hear the news first keep it locked on to the Official Forums.

(Source - Batman: Arkham Asylum Forum)