  In representations using frames, oblique duality appears in situations where
the analysis and the synthesis has to be done in different subspaces. In some
cases, we cannot obtain an explicit expression for the oblique duals and in
others there exists only one oblique dual frame which has not the properties we
need. Also, in practice the computations are not exact. To give a solution to
these problems, in this work we introduce and investigate the notion of
approximate oblique dual frames first in the setting of separable Hilbert
spaces. We focus then on approximate oblique dual frames in shift-invariant
subspaces of L^2(R). We give different conditions on the generators that assure
the existence of approximate oblique dual frames. We present an example that
illustrates the results.
