Abstract
We discuss a covariant decomposition of gauge fields into gauge-invariant physical components and gauge-dependent unphysical components. In particular, we consider QED with nonlinear gauge conditions and Yang-Mills gravity with 4-dimensional translational gauge symmetry (T(4) group) in flat space-time. The consistency and intimate relations among decomposition of gauge fields for all times, and gauge conditions and Faddeev-Popov ghost fields are investigated. The gauge invariance of QED and Yang-Mills gravity are revealed by the invariance of physical components under gauge transformations.