  Let $k$ be a field of characteristic $0$. We consider principal bundles over
a $k$-scheme with reductive structure group (not necessarily of finite type).
It is showm in particular that for $k$ algebraically closed there exists on any
complete connected $k$-scheme a universal such bundle. As a consequence, an
explicit description of principal bundles with reductive structure group over
curves of genus $0$ or $1$ is obtained.
