The adsorption reaction of acetylene on the Ge(001) surface is investigated by first-principles calculations. In order to understand the relative populations of the di-σ and paired-end-bridge structures, we calculated the adsorption reaction paths leading to their formation at 0.5 and 1.0 ML coverage. More importantly, we studied the adsorption channel involving sublayer Ge atoms by forming a metastable subdi-σ structure. This sub-di-σ structure represents second reaction pathway that results in the end-bridge structure, which plays an important role in the formation of the adsorption configurations. In contrast to C2H2, the adsorption of C2H4 on the Ge(001) surface involving subsurface Ge atoms, is endothermic. Our calculations show from both kinetic and thermodynamic standpoints that the paired-end-bridge structure is the primary adsorption configuration that explains the experimental observations. Our work also helps to understand the fundamental differences between the adsorption of C2H2 and C2H4 on the Ge(001) surface.