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A complete description of the linearized gravitational field on a flatbackground is given in terms of gauge-independent quasilocal quantities. Thisis an extension of the results from gr-qc/9801068. Asymptotic sphericalquasilocal parameterization of the Weyl field and its relation with Einsteinequations is presented. The field equations are equivalent to the waveequation. A generalization for Schwarzschild background is developed and theaxial part of gravitational field is fully analyzed. In the case of axialdegree of freedom for linearized gravitational field the correspondinggeneralization of the d'Alembert operator is a Regge-Wheeler equation. Finally,the asymptotics at null infinity is investigated and strong peeling propertyfor axial waves is proved.Comment: 27 page

$lquot$Peeling property$rquot$ for linearized gravity in null coordinates