A dynamical system with delay described by the following functional differential equation with delay \[ \dot x(t)=f(t,x_t).\tag{1} \] is considered. Suppose that \(f(t,0)\equiv 0\) for all \(t\in\mathbb{R}\), so that \(x^*\equiv 0\) is an equilibrium point of system (1). Theorem. Let \(\lambda\) and \(p\) be positive constants, \(p\geq 1\), \(\alpha:J \to\mathbb{R}_+\) be a continuous positive function, \(V:\mathbb{R}\times \mathbb{R}^n\to \mathbb{R}_+\) be a continuous function, \(\lambda\| x\|^p\leq V(t,x)\) for \((t,x)\in \mathbb{R}\times \mathbb{R}^n\), and \(V(t,x)\) be bounded for given \(x\in\mathbb{R}^n\). The equilibrium \(x^*\equiv 0\) of system (1) is globally exponentially stable with respect to the time-varying delay with power \(\alpha(t)/p\) on \(t\geq t_0\) if along the solution \(x(t_0, \varphi)(t)\) of system (1) through \((t_0,\varphi)\in J\times C_n\) \[ \dot V\bigl( t,x(t)\bigr)\leq -\alpha (t)V\bigl(t,x(t) \bigr) \] whenever \(V(t,x(t))= \overline V_{t_0}\exp \{-\int^t_{t_0} \alpha(t)dt\}\), \(t\geq t_0\).