A device of an engine having a plurality of cylinders includes: exhaust passages each connected with either a single cylinder or two or more cylinders having non-adjacent exhaust order; a manifold section connected with each downstream end of the exhaust passages; a catalyst device downstream of the manifold section; and a valve driver. Within a low-speed and high-load engine operating range, the valve driver drives intake and exhaust valves of each cylinder such that, for a particular cylinder, a period of positive valve overlap overlaps an exhaust valve opening time of another cylinder adjacent in the exhaust order. The manifold section includes a part that reduces in diameter downstream from the upstream end of the manifold section, and a straight part with a substantially fixed flow area extending upstream from the downstream end of the manifold section. In this way, negative pressure may be generated due to an ejector effect.