  We consider scalar delay differential equations $x'(t) = -\delta x(t) +
f(t,x_t) (*)$ with nonlinear f satisfying a sort of negative feedback condition
combined with a boundedness condition. The well known Mackey-Glass type
equations, equations satisfying the Yorke condition, equations with maxima are
kept within our considerations. Here, we establish a criterion for the global
asymptotical stability of a unique steady state to $(*)$. As an example, we
study Nicholson's blowflies equation, where our computations support Smith's
conjecture about the equivalence of global and local asymptotical stability in
this population model.
