Mixtures of methyltetrahydrofuran (MTHF) with tristyrene and high molecular weight polystyrene involve an exceptionally large difference in the glass transition temperatures of the two components not realized in other binary Mixtures studied before. The extensive study of the molecular dynamics of these mixtures by various experimental techniques by Blochowicz et al. has revealed the presence of a new alpha'-relaxation not found before in other mixtures and also the more familiar alpha- and beta-relaxations, but their properties are More extreme. Attention was focused on the new alpha'-relaxation by Blochowicz et al. in interpreting it to originate from MTHF in confinement and explaining its properties by the Mode Coupling Theory. In a different direction, we concentrate on the highly unusual properties of the alpha- and beta-relaxations. Earlier, we had success in explaining the properties of these two relaxations and their connection in other mixtures by the coupling model. In this paper, we apply the same model to explain the highly unusual dynamics of the alpha- and beta-relaxations found in the mixtures of MTHF with tristyrene and polystyrene. Possible relation between the alpha'- and the beta-relaxations also is explored.