In this paper, we study the notions of approximate biprojectivity, approximate biflatness and approximate Connes biprojectvity of some Banach algebras. We show that the Segal algebra S(G) is approximately biprojective (approximate biflat) if and only if G is compact(amenable), respectively. Also we give a class of matrix algebras which is neither approximate biprojective nor is approximate biflat. We show that the measure algebra over a locally compact group G is approximately biprojective if and only if G is amenable.
