The hydriding and dehydriding properties of the quarternary Zr1-xTixMnFe and Zr1-xTixV0.5Fe1.5 Laves phase alloys for the range 0 less-than-or-equal-to x less-than-or-equal-to 0.3 were investigated as a function of alloy concentration. In addition, by comparing previously reported data on the Zr1-xTixCr1-yFe1+y system with those of the above two systems, the effect of alloying elements (e.g. titanium and iron) on the behaviour of the plateau slope was systematically analysed in order to understand the origin of sloping plateaux in the zirconium-based Laves phase. As titanium substitutes for zirconium in the Zr1-xTixMnFe alloys, the slopes of the linearly increasing plateaux become lower with increasing hydrogen concentration. Unlike the ZrCr2-base system, well-defined plateaux appear at x = 0.2 and a further increase in x to 0.3 produces an increase in the plateau slope. However, in the Zr1-xTixV0.5Fe1.5 system, titanium substitution does not cause any significant change in the plateau slope. From investigations of the lattice strain of each type of alloy system, it is found that the variations in the degree of slope with alloy composition is closely associated with the lattice strain of alloy caused by elemental substitution. It is suggested from the above results that the sloping plateaux in the zirconium-based Laves phase originates from the difference between the energy levels of various interstitial sites with respect to hydrogen where the energy level of each site is determined from the combined effects of two factors: a chemical energy and a strain energy.