In this paper, we construct the sequences of the sheaves of homotopy groups of a pair (XA) and of a tıiple (XA3), where X is a connected, locally path connected, and semilocally simply connected topological space and A, B are both öpen connected, locally path connected, and semilocally simply connected subspaces of X with B c A c X. Furthermore, we prove the existence of a homomorphism induced by a continuous map f: (XA) (Y3) (respectively, f: (X,A3) —> (Y,C,D)) between the sequences of the sheaves of homotcçy groups of the pairs (XA) and (Y,B) (respectively, of the triples (XA,B) and (Y,C,a)).