  We present the covariance analysis of two successful nuclear energy density
functionals, (i) a non-relativistic Skyrme functional built from a zero-range
effective interaction, and (ii) a relativistic nuclear energy density
functional based on density dependent meson-nucleon couplings. The covariance
analysis is a useful tool for understanding the limitations of a model, the
correlations between observables and the statistical errors. We show, for our
selected test nucleus 208Pb, that when the constraint on a property A included
in the fit is relaxed, correlations with other observables B become larger; on
the other hand, when a strong constraint is imposed on A, the correlations with
other properties become very small. We also provide a brief review, partly
connected with the covariance analysis, of some instabilities displayed by
several energy density functionals currently used in nuclear physics.
