  We consider the valued field $\mathds{K}:=\mathbb{R}((\Gamma))$ of
generalized series (with real coefficients and monomials in a totally ordered
multiplicative group $\Gamma$). We investigate how to endow $\mathds{K}$ with a
series derivation, that is a derivation that satisfies some natural properties
such as commuting with infinite sums (strong linearity) and (an infinite
version of) Leibniz rule. We characterize when such a derivation is of Hardy
type, that is, when it behaves like differentiation of germs of real valued
functions in a Hardy field. We provide a necessary and sufficent condition for
a series derivation of Hardy type to be surjective.
