Hydrogen absorption isotherms have been obtained for the C14-type hexagonal-structured alloys ZrMnFe1-xCox (x = 0.2, 0.4, 0.5 and 0.6) in the temperature and pressure ranges 30 ≤ T/°C ≤ 100 and 0.1 ≤ P/bar ≤ 40 using a high-pressure unit based on the pressure reduction method. The powder x-ray diffractograms show that the lattice constants and the unit-cell volume for ZrMnFe1-xCox (x = 0.2, 0.4, 0.5 and 0.6) alloys decrease with increase of XCo. The hydrogen absorption isotherms show the presence of a single plateau region (α + β) in the temperature and pressure ranges studied and it is found that the plateau pressure and plateau slope at any given temperature increase with increase of the XCo-Content, except in the case of ZrMnFe0.5Co0.5 wherein the hydrogen absorption plateau slope is found to be smaller due to the ordering of the alloy. The dependence of the thermodynamics of the dissolved hydrogen in ZrMnFe1-xCox-H (x = 0.2, 0.4, 0.5 and 0.6) systems in the temperature range 30-50 °C on the hydrogen concentration shows the different phase regions (α, α + β, β) seen in the hydrogen absorption isotherms. The powder x-ray diffractograms of the hydrides of ZrMnFe0.8Co0.2 show that the formation of different phases is manifested in the isotherms without there being any structural change and the inclusion of hydrogen in the interstitial sites expands the unit-cell volume by about 21%. Comparison of the hydrogen absorption kinetics of ZrMnFe1-xCox with that of the corresponding Ni alloys in similar experimental conditions shows that the kinetics is slow in the ZrMnFe1-xCox alloys.