Display characterization is one of the key-problems for colour management, and in the early stage focus is on developing transforms between the display digital driving signals RGB and the colorimetric values XYZ. The GOG and PLCC models were widely considered for this kind of applications in the literature. Recently, in order to reproduce colour match in spectral, display spectral characterization becomes a hot research topic, which has a very important application for the reproduction of multispectral images. In this paper, the well-known GOG and PLCC models are proposed for spectral characterization for the liquid crystal displays. Though the GOG and PLCC models have been widely considered for the display characterization application, it seems that there are no discussions for the display spectral characterization in the literature. It is first shown in this paper that the GOG and PLCC models can indeed be used for display spectral characterization under the assumptions of channel independence and chromaticity constancy for each channel. Performance of the proposed models together with SRPM and SRPPM models are considered using the two widely used professional displays: EIZO CG277 and BENQ PG2401 LCD. At the same time, comparisons are also considered for the GOG and PLCC models trained using the pure red/green/blue colour data and the grey scale (neutral point) data respectively. The comparison results have shown that both GOG and PLCC perform better trained using the grey scale (neutral point) data than those trained using the pure red/green/blue colour data. Furthermore, the comparison results have also shown that PLCC model trained using the grey scale (neutral-point) data performs better than the SRPPM and GOG models according to both forward and inverse models. Especially, the inverse of the PLCC model is much simpler than the inverse of the SRPPM model. Hence the PLCC model is recommended for the LCD spectral characterization.