The authors are concerned with the following delay differential equation \[ v^{\prime}=L(t)v_t+g(t,v_t),\tag{E} \] where \(L(t):C([-r,0];\mathbb{R}^n)\to \mathbb{R}^n\), \(t\in \mathbb{R}\), are bounded linear operators (here \(r\) is a positive number) satisfying \(\sup_{t\in \mathbb{R}}\int_t^{t+1}\Vert L(s) \Vert ds < \infty\), and \(g=g(t,v):\mathbb{R}\times C([-r,0]; \mathbb{R}^n) \to \mathbb{R}^n\) is a \(C^k\) map with \(g(t,0)=0\), \(\partial g(t,0)=0\) for all \(t\in \mathbb{R}\), where \(\partial\) denotes the partial derivative of \(g\) with respect to the second variable. As usual, \(v_t(\theta)=v(t+\theta)\), \(\theta \in [-r,0]\), \(t\in \mathbb{R}\). The authors give a detailed proof of the existence of smooth center invariant manifolds for Eq. (E) in the case when the linear part has an exponential trichotomy. If \(g(t, \cdot)\) has Lipschitz \(k\)-th deriative, the same regularity is obtained for the center manifolds.