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In this study, two finite-difference time-domain algorithms are proposed for time domain analysis of the lossy non-uniform composite right/left-handed transmission line (CRLH TL). The results of the proposed algorithm are confirmed with those of the ADS commercial software. The numerical stability of the proposed algorithms is studied and a closed form formula for maximum temporal step size that guarantees algorithm stability is extracted. Finally, a new algorithm for time-domain analysis of the non-linear CRLH TLs using finite-difference time-domain is proposed. This algorithm does not impose any limitation on type of non-linearity. The results of the proposed algorithm have a good agreement with the results of the ADS commercial software.