Ab initio total energy calculations by means of the FLEUR code, an implementation of the FP-LAPW method, indicate that the ground states of LaMn₂Ge₂ and LaMn₂Si₂ exhibit noncollinear magnetism in agreement with the low temperature experimental data. Despite the difference between the calculated and measured canting angles, the trend is well reproduced by the theory. Preliminary calculations using the generalized Bloch's theorem leads to a spin spiral in LaMn₂Ge₂.