The Si(113) surface has been investigated using video low-energy electron diffraction (LEED), angle-resolved UV photoelectron spectroscopy (ARUPS), and high-resolution electron energy-loss spectroscopy (HREELS) of hydrogen adsorption. At 300 K we find a 3 x 2 reconstruction for the clean Si(113) surface. Hydrogen adsorption proceeds in two steps. During the first step only Si-H bonds are formed, the photoemission from the dangling bonds becomes completely quenched and the 3 x 2 structure is transformed into a 3 x 1-H. These results strongly indicate that the 3 x 2 --> 3 x 1-H transformation proceeds without bond proceeds without bond breaking and Si transport. In the second step Si-H2 is formed in addition to Si-H and the reconstruction is changed from 3 x 1-H to 1 x 1. We discuss a model for the 3 x 2 structure in which the number of dangling bonds is largely reduced and an easy 3 x 2 --> 3 x 1-H transformation is possible. However, a model that meets all experimental demands is still lacking.