Concerned that your partner may be cheating on you? There are two scenarios that may be at play here; either you are paranoid (which also contains two sub scenarios) or they are truly cheating on you.
If they are truly cheating on you; you have caught them, they admitted to it, you have hard evidence that they are cheating on you, then, you must confront them about this and talk about it. If they feel that they still want to continue the relationship and feel profoundly sorry about sleeping (or what have you) with another, then, there may be hope. If this is the first time it has occured, then there could be room for forgiveness and understanding. This is, of course, given that there is a very good excuse for whatever they did (commonly alcohol or some impartment) and you can understand their motivations for whatever they did, and you feel that it will not happen again, then perhaps forgiveness and a second chance is applicable. Although, if this is the second time it has happened, and they are still trying to ask for forgiveness, then, I would suggest to end the relationship. If it has happened twice now, then there is promiscuous problems and mis-trust has developed very quickly. Unless they have a VERY GOOD reason for doing what they did, a second time, then I see no other option than to end the relationship, for they are seeking attention elsewhere and not you; they are being with other people and flirting, etc. with others; not you. This isn't much of a relationship.
If you only think they might be cheating on you, then there are two sub scenarios that may apply. First, you may be paranoid and causing problems for yourself. See the explanation for paranoia for dumping here.