It depends on how serious you and the new beau are. If he's just a rebound fling that you're kicking up your heels with, the answer would be never. Never introduce a casual partner to your children, unless you plan to do so ONLY as though that person is strictly on the "friend only" level and your children will never see you exchange intimate gestures with each other.
Otherwise, it depends on how old your kids are, how emotionally mature they are, how traumatized they have been from your divorce, whether or not they have a good relationship with their dad, whether or not you (or their father) uses them as pawns in a "tit for tat" game of spite against each other....and the list goes on.
Your ONLY priority should be to your children, first and foremost. If you are playing hide the sausage with another man and contemplating bringing him into your children's lives, it should be YOUR CHILDREN that determine when they are ready to meet a new "uncle."