See if he starts thinking more about his appearance. If your boyfriend's wardrobe suddenly triples to more during the last two months, but you almost never date, then he might dress up for someone other than you. Can be a co-worker, classmate, or someone in his life. And when he suddenly spends more time when arranging his hair and dressing up when he says he just wants to go shopping or drink coffee with his friend, then maybe something has happened.
If he suddenly spends more time in the gym and is far more interested in getting a good body shape, maybe he does it for someone else.
Just to clarify - he might just start to care about his appearance because he wants to look better and fitter. But at this point, coupled with the presence of others, can be a sign of an affair.