In order to correct different numbers of erasures in distributed storage systems, the design of locally repairable codes with hierarchical locality (H-LRCs) is crucial. In this paper, we study h-level H-LRCs where h is not limited to 2. We present four constructions of cyclic h-level H-LRCs with length ln₁ such that gcd(l, q) = 1 and n₁|(q−1). These four classes of cyclic h-level H-LRCs are optimal with respect to the generalized Singleton-like bound. The minimum Hamming distances of them are d = δ₁, δ₁+1, δ₁+2, δ₁+δ_h respectively. Furthermore, these four classes of cyclic h-level H-LRCs have new and flexible parameters which are not covered in the literature. By setting the parameter l appropriately for the third construction, one can construct optimal cyclic h-level H-LRCs with length n|(q−1) and distance d = δ₁+σ where σ is not limited to 0, 1, 2, δ_h.