Summary: In this work, we establish conditions to guarantee the permanence of the solution of the Nicholson's blowflies model with delay \[ \begin{cases} x'(t)=-\delta(t)x(t)+R(t)x(t-\tau(t))\exp[-a(t)x(t-\tau(t))],\quad t>0,\\ x(t)=\varphi(t),\quad t\in[-r,0], \end{cases} \] where \(R,\tau:\mathbb{R}\to[0,\infty)\) are bounded continuous functions, \(r=\sup_{t\in\mathbb{R}}\tau(t)\), \(\varphi:[-r,0]\to[0,\infty)\) is a continuous function with \(\varphi(0)>0\), and \(\delta,a:\mathbb{R}\to(0,\infty)\) are bounded continuous functions. More specifically, we will be interested in obtaining positive constants \(k\) and \(K\) such that, if \(x:[-r,\infty)\to\mathbb{R}\) is the solution of the described system, then \(k\leq\lim_{t\to\infty}\operatorname{inf}x(t)\leq\lim_{t\to\infty}\sup x(t)\leq K\). Some numerical examples are provided to illustrate our results.