  The Matrix Element Method (MEM) has proven beneficial to make maximal use of
the information available in experimental data. However, so far it has mostly
been used in Born approximation only. In this paper we discuss an extension to
NLO accuracy. As a prerequisite we present an efficient method to calculate
event weights for jet events at NLO accuracy. As illustration and proof of
concept we apply the method to the extraction of the top-quark mass in e+e-
annihilation. We observe significant differences when moving from LO to NLO
which may be relevant for the interpretation of top-quark mass measurements at
hadron colliders relying on the MEM.
