In this paper, we show the existence of Landau and Bloch constants for biharmonic mappings of the form L (F). Here L represents the linear complex operator L = z frac(∂, ∂ z) - over(z, ̄) frac(∂, ∂ over(z, ̄)) defined on the class of complex-valued C1 functions in the plane, and F belongs to the class of biharmonic mappings of the form F (z) = | z |2 G (z) + K (z) (| z | < 1), where G and K are harmonic. Crown Copyright © 2008.