  A general nonautonomous Nicholson equation with multiple pairs of delays in
{\it mixed monotone} nonlinear terms is studied. Sufficient conditions for
permanence are given, with explicit lower and upper uniform bounds for all
positive solutions. Imposing an additional condition on the size of some of the
delays, and by using an adequate difference equation of the form
$x_{n+1}=h(x_n)$, we show that all positive solutions are globally attractive.
In the case of a periodic equation, a criterion for existence of a globally
attractive positive solution is provided. The results here constitute a
significant improvement of recent literature, in view of the generality of the
equation under study and of sharper criteria obtained for situations covered in
recent works. Several examples illustrate the results.
