Precipitation of two Laves phases, C14 and C15 Mg2Nd phases, is reported for the first time in a Mg-Nd-Ca alloy isothermally aged at 250 °C. Both Laves phases form as basal precipitate plates, and their orientation relationships with the α-Mg matrix are (0001)C14//(0001)α, [21¯1¯0]C14//[011¯0]α and (1¯11)C15//(0001)α, [211]C15//[2¯110]α, respectively. The C14 Mg2Nd Laves phase can form without the involvement of shear displacement, while the formation of a C15 Mg2Nd Laves phase is invariably associated with an I1 stacking fault that is bounded by two self-accommodating Frank partial dislocations. For these two Laves phases, their triangular nets are transformed from the matrix lattice by the ordered substitution of Nd for selected Mg atoms and the atomic shuffle of Nd atoms along the <0001>α directions, and their kagome nets can be formed by the atomic shuffle of Mg atoms along three crystallographically equivalent <011‾0>α directions.