  Let $ k $ be a field, $ G $ a totally ordered abelian group and $ \mathbb K =
k((G)) $ the maximal field of generalised power series, endowed with the
canonical valuation $ v $. We study the group $ v \mathrm{-Aut} K $ of
valuation preserving automorphisms of a subfield $ k(G)\subseteq K\subseteq
\mathbb K $, where $ k(G) $ is the fraction field of the group ring $ k[G] $.
Under the assumption that $ K $ satisfies two lifting properties we are able to
generalise and refine Hofberger's decomposition of $ v \mathrm{-Aut}\mathbb K $
and prove a structure theorem decomposing $ v\mathrm{-Aut} K $ into a 4-factor
semi-direct product of notable subgroups. We then identify a large class of
Hahn fields satisfying the two aforementioned lifting properties. Next we focus
on the group of strongly additive automorphisms of $ K $. We give an explicit
description of the group of strongly additive internal automorphisms in terms
of the groups of homomorphisms $ \mathrm{Hom}(G,k^\times) $ of $ G $ into $
k^\times $ and $ \mathrm{Hom}(G,1+I_K) $ of $ G $ into the group of 1-units of
the valuation ring of $ K $. Finally, we specialise our results to some
relevant special cases. In particular, we extend the work of Schilling on the
field of Laurent series and that of Deschamps on the field of Puiseux series.
