1. [for a host or hostess] to invite someone to come again (at a later time or to another similar event). After the way you behaved, they'll never ask us back. They had been asked back a number of times, but they never came.

2. [for someone who has been a guest] to invite a previous host or hostess to come to an event. We've had the Smiths to dinner five times. I think it's time they asked us back. I don't care if they ask us back or not.