The performance of physical-layer network coding (PLNC) in two way relay channels (TWRCs) is significantly decreased by impairments like carrier frequency offsets or timing offsets. This mismatch cannot be completely compensated at the receiver side, even if the offsets are known. Multi-carrier systems with Gaussian waveforms for TWRC systems are more robust against the impact of these offsets. In comparison to rectangular multi-carrier systems, Gaussian waveforms have a better time-frequency shape and they provide improved spectral  efficiency due to lower out of band radiations. In this paper, we introduce a multi-carrier TWRC system with Gaussian waveforms and develop an adapted soft interference cancellation (SIC) equalizer to consider the intrinsic  interference of the Gaussian transmit/receive filters. The presented results show, that systems with Gaussian waveforms achieve bit error rates close to the rectangular waveforms in PLNC systems while being more robust against Doppler and delay spreads.