Let D=(V(D),A(D)) be a digraph and k≥2 be an integer. A vertex x is a k-king of D, if for every y∈V(D), there is an (x,y)-path of length at most k. A subset N of V(D) is k-independent if for every pair of vertices u,v∈N, we have d(u,v)≥k and d(v,u)≥k; it is l-absorbent if for every u∈V(D)−N, there exists v∈N such that d(u,v)≤l. A (k,l)-kernel of D is a k-independent and l-absorbent subset of V(D). A k-kernel is a (k,k−1)-kernel.A digraph D is k-quasi-transitive, if for any path x0x1…xk of length k, x0 and xk are adjacent. Recently, we have shown that a k-quasi-transitive digraph with k≥4 has a k-king if and only if it has a unique initial strong component D1 and D1 is not isomorphic to an extended (k+1)-cycle. In this article, we will study the number of k-kings in a k-quasi-transitive digraph when it has a k-king. Indeed, we show that when k=4, it may have exactly one 4-king; if k≥5, then it has at least two k-kings. In addition, we obtain new results on the minimum number of (k+1)-kings in k-quasi-transitive digraphs.Galeana-Sánchez et al. conjectured that every k-quasi-transitive digraph has a (k+1)-kernel. In this article, we shall prove that the conjecture is true.