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The Bisognano-Wichmann property for local, Poincare covariant nets of standard subspaces is discussed. We present a sufficient algebraic condition on the covariant representation ensuring Bisognano-Wichmann and Duality properties without further assumptions on the net. Our “modularity” condition holds for direct integrals of scalar massive and masselss representations. We conclude that in these cases the BisognanoWichmann property is much weaker than the Split property. Furthermore, we present a class of massive modular covariant nets not satisfying the Bisognano-Wichmann property.

An algebraic condition for the Bisognano-Wichmann property