We consider the integro-differential operator equations having the form
$$\sum\limits_{i=1}^n\alpha_iu^{(i)}(t)-\alpha Au(t)+\beta \mu \ast u(t)=f(t), \quad t\in\mathbb R,$$
where the free term $f$ belongs to a closed subspace $M$ of $L^{\infty}(\mathbb R,X)$, $A$ is the generator of a $C_0$-semigroup of operators defined on a Banach space $X$, $\mu$ is a bounded Borel measure on $\mathbb R$ and $\alpha,\beta,\alpha_i\in\mathbb C$, $i=1,2,\dots,n$. Certain conditions will be imposed to guarantee the existence of solutions in the class $M$.