First-principles plane wave calculations have been performed to study the adsorption of alkali and alkaline earth metals on monolayer germanium carbide (GeC). We found that the favourable adsorption sites on GeC sheet for single alkali and alkaline earth adatoms are generally different from graphene or germanene. Among them, Mg, Na and their dimers have weakly bounded to GeC due to their closed valence electron shells, so they may have high mobility on GeC. Two different levels of adatom coverage (theta = 1/8 and theta = 1/32) have been investigated and we concluded that different electronic structures and magnetic moments for both coverages owing to alkali and alkaline earth atoms have long range electrostatic interactions. Lithium atom prefers to adsorbed on hollow site similar to other group-IV monolayers and the adsorption results in metallisation of GeC instead of semiconducting behaviour. Na and K adsorption can induce 1 mu B total magnetic moment on GeC structures and they have shown semiconductor property which may have potential use in spintronic devices. We also showed that alkali or alkaline earth metal atoms can form dimer on GeC sheet. Calculated adsorption energies suggest that clustering of alkali and alkaline earth atoms is energetically favourable. All dimer adsorbed GeC systems have nonmagnetic semiconductor property with varying band gaps from 0.391 to 1.311 eV which are very suitable values for various device applications.