  We show that \'Ecalle's transseries and their variants (LE and EL-series) can
be interpreted as functions from positive infinite surreal numbers to surreal
numbers. The same holds for a much larger class of formal series, here called
omega-series. Omega-series are the smallest subfield of the surreal numbers
containing the reals, the ordinal omega, and closed under the exp and log
functions and all possible infinite sums. They form a proper class, can be
composed and differentiated, and are surreal analytic. The surreal numbers
themselves can be interpreted as a large field of transseries containing the
omega-series, but, unlike omega-series, they lack a composition operator
compatible with the derivation introduced by the authors in an earlier paper.
