Generalized power series extend the notion of formal power series by considering
exponents of each variable ranging in awell ordered set of positive real numbers.Generalized
analytic functions are defined locally by the sum of convergent generalized power series
with real coefficients. We prove a local monomialization result for these functions: they can
be transformed into a monomial via a locally finite collection of finite sequences of local
blowings-up. For a convenient framework where this result can be established, we introduce
the notion of generalized analytic manifold and the correct definition of blowing-up in this
category.
