  We construct an explicit minimal model for an algebra over the
cobar-construction of a differential graded operad. The structure maps of this
minimal model are expressed in terms of sums over decorated trees. We introduce
the appropriate notion of a homotopy equivalence of operadic algebras and show
that our minimal model is homotopy equivalent to the original algebra. All this
generalizes and gives a conceptual explanation of well-known results for
A-infinity algebras. Further, we show that these results carry over to the case
of algebras over modular operads; the sums over trees get replaced by sums over
general Feynman graphs. As a by-product of our work we prove gauge-independence
of Kontsevich's `dual construction' producing graph cohomology classes from
contractible differential graded Frobenius algebras.
