The magnetic properties of a set of LaFe13−x−yCoySix compounds (x = 1.6 − 2.6; y = 0, y = 1.0) have been investigated using magnetic measurements, thermal expansion, 57Fe Mössbauer spectroscopy and high resolution neutron powder diffraction methods over the temperature range 10–300 K. The natures of the magnetic transitions in these LaFe13−x−yCoySix compounds have been determined. The Curie temperatures of LaFe13−xSix were found to increase with Si content from TC = 219(5) K for Si content x = 1.6 to TC = 250(5) K for x = 2.6. Substitution of Co for Fe in LaFe10.4Si2.6 resulted in a further enhancement of the magnetic ordering temperature to TC = 281(5) K for the LaFe9.4CoSi2.6 compound. The nature of the magnetic transition at the Curie temperature changes from first order for LaFe11.4Si1.6 to second order for LaFe10.4Si2.6 and LaFe9.4CoSi2.6. The temperature dependences of the mean magnetic hyperfine field values lead to TC values in good agreement with analyses of the magnetic measurements. The magnetic entropy change, −ΔSM, has been determined from the magnetization curves as functions of temperature and magnetic field (ΔB = 0 − 5 T) by applying the standard Maxwell relation. In the case of LaFe12.4Si1.6 for example, the magnetic entropy change around TC is determined to be -ΔSM ∼ 14.5 J kg−1 K−1 for a magnetic field change Δ B = 0 − 5 T.