The paper focuses on the classes of the k-generalized and k-hypergeneralized projectors. Several original features of these classes are identified and new properties are characterized. We present some relations between k-generalized and k-hypergeneralized projectors that generalize appropriate relations between generalized and hypergeneralized projectors given in [Further properties of generalized and hypergeneralized projectors, Linear Algebra and its Applications, 389 (2004) 295–303] and [Further results on generalized and hypergeneralized projectors, Linear Algebra and its Applications, 429 (2008) 1038–1050].