1. Introduction A singularly perturbed differential-difference equation (DDE) is an ordinary differential equation in which the highest derivative is multiplied by a small parameter and including at least one delay term. More particularly, singularly perturbed delay differential initial or boundary value problems (BVPs) arise in modelling of the study of human pupil light reflex [26], first-exit problems in neurobiology [32], models of physiological processes and diseases [27], optimal control theory [12], optically bistable devices [5] and signal transmission [7], and other models [8]. However, DDEs in the regular case often appear in various phenomena in science and engineering such as dynamical diseases, population ecology, economics, biosciences [4, 6, 10, 11, 13, 25, 33]. Furthermore, some existence and uniqueness of solution to DDEs are discussed in [3, 14, 15, 16, 22, 23, 29]. In [19, 20, 21] authors have been discussed an asymptotic approach to analyze of BVPs for second order singularly perturbed DDEs. Moreover, some numerical viewpoints of this type of problems with small delay term are considered in [17, 18] and only the convection term is included in [24, 28]. The structure of this paper is as follows. In Section 2, the problem of study is stated. The main results are established in Section 3, and in Section 4, an example is presented to illustrate the theoretical results obtained.