  In this paper we aim for a generalisation of the Steenrod Approximation
Theorem from, concerning a smoothing procedure for sections in smooth locally
trivial bundles. The generalisation is that we consider locally trivial smooth
bundles with a possibly infinite-dimensional typical fibre. The main result
states that a continuous section in a smooth locally trivial bundles can always
be smoothed out in a very controlled way (in terms of the graph topology on
spaces of continuous functions), preserving the section on regions where it is
already smooth.
