  The problem considered in the paper is exponential stability of linear
equations and global attractivity of nonlinear non-autonomous equations which
include a non-delay term and one or more delayed terms. First, we demonstrate
that introducing a non-delay term with a non-negative coefficient can destroy
stability of the delay equation. Next, sufficient exponential stability
conditions for linear equations with concentrated or distributed delays and
global attractivity conditions for nonlinear equations are obtained. The
nonlinear results are applied tothe Mackey-Glass model of respiratory dynamics.
