Suppose that (T, *) is a groupoid with a left identity such that each element a ∈ T has a left inverse. Then T is called a gyrogroup if and only if (i) there exists a function gyr : T x T → Aut(T) such that for all a,b,c ∈ T, a* (b * c) = (a * b) * gyr[a,b]c, where gyr[a,b]c = gyr(a,b)(c); and (ii) for all a,b ∈ T, gyr[a,b] = gyr[a * b,b]. In this paper, the structure of normal subgyrogroups of certain gyrogroups are investigated.