The nut slots might be too wide, or not cut with a sufficient angle that the strings take off from the front edge of the nut. Or, even simpler (I've found this a few times), just build up of gunge in the nut slot. Try cleaning the slot with a file, or a bit of fine sandpaper... Then check the angle of the slot. If that doesn't work, try filling and recutting the slot with the proper sized nut file.
What Martin says seems like good advice. If you want to refill the nut slot so that you can cut it again, do you know the baking soda and superglue trick? Google it if you don't. It is a time honoured way to rescue a nut with one bad slot.