In this paper, we introduce the Cognitive Multiple Access Z Interference Channel (CMAZIC) where there are two secondary user (SU) transmitters and one SU receiver and one primary user (PU) transceiver pair. Both the SUs are aware of the PU message non causally. There is interference only from the PU transmitter to the SU receiver but not vice versa. We study the Discrete Memoryless CMAZIC (DM-CMAZIC) and provide achievable rate regions with and without superposition coding at the PU transmitter and with Gelfand Pinsker coding against the interference of the PU at both the SU transmitters. For the Gaussian case we show that the inner bound without superposition coding is capacity achieving when appropriate Dirty paper coding is performed at the SU transmitters. © 2014 IEEE.