A channel model for secret key generation between three terminals is considered. In this model, there is a two-user generalized multiple access channel (MAC) in which, in addition to the receiver, both transmitters receive noisy channel outputs. There is also a one-way public channel from the transmitters to the receiver. In this model, each of the transmitters intends to share a secret key with the receiver using the MAC and the public channel where the transmitters are eavesdroppers with respect to each other. In this setup, the channel outputs at the transmitters are only used for eavesdropping and not as inputs to the encoders. For the secret key rate pair, we derive the inner bound of the secret key capacity region. Thorough an example, it is shown that unlike the broadcast channel model, using a one-way public channel from the transmitters to the receiver is beneficial.