  We classify nonabelian extensions of Lie algebroids in the holomorphic
category. Moreover we study a spectral sequence associated to any such
extension. This spectral sequence generalizes the Hochschild-Serre spectral
sequence for Lie algebras to the holomorphic Lie algebroid setting. As an
application, we show that the hypercohomology of the Atiyah algebroid of a line
bundle has a natural Hodge structure.
