The fading cognitive multiple-access channel with confidential messages (MAC-CM) is investigated, in which two users attempt to transmit common information to a destination and user 1 also has confidential information intended for the destination. User 1 views user 2 as an eavesdropper and wishes to keep its confidential information as secret as possible from user 2. The multiple-access channel (both the user-to-user channel and the user-to-destination channel) is corrupted by multiplicative fading gain coefficients in addition to additive white Gaussian noise. The channel state information (CSI) is assumed to be known at both the users and the destination. A parallel MACCM with independent subchannels is first studied. The secrecy capacity region of the parallel MAC-CM is established, which gives the secrecy capacity region of the parallel MAC-CM with degraded subchannels. Next, the secrecy capacity region is established for the parallel Gaussian MAC-CM, which is used to study the fading MAC-CM. By assuming both users know the CSI, users can dynamically change their transmission power with the channel realization to achieve the best performance.