We study a two-user state-dependent generalized multiple-access channel (GMAC) with correlated states. It is assumed that each encoder has \emph{noncausal} access to channel state information (CSI). We develop an achievable rate region by employing rate-splitting, block Markov encoding, Gelfand--Pinsker multicoding, superposition coding and joint typicality decoding. In the proposed scheme, the encoders use a partial decoding strategy to collaborate in the next block, and the receiver uses a backward decoding strategy with joint unique decoding at each stage. Our achievable rate region includes several previously known regions proposed in the literature for different scenarios of multiple-access and relay channels. Then, we consider two Gaussian GMACs with additive interference. In the first model, we assume that the interference is known noncausally at both of the encoders and construct a multi-layer Costa precoding scheme that removes \emph{completely} the effect of the interference. In the second model, we consider a doubly dirty Gaussian GMAC in which each of interferences is known noncausally only at one encoder. We derive an inner bound and analyze the achievable rate region for the latter model and interestingly prove that if one of the encoders knows the full CSI, there exists an achievable rate region which is \emph{independent} of the power of interference.