This paper introduces generalized Clifford and Lipschitz groups in degenerate geometric (Clifford) algebras. These groups preserve the direct sums of the subspaces determined by the grade involution and the reversion under the adjoint and twisted adjoint representations. We prove that the generalized degenerate Clifford and Lipschitz groups can be defined using centralizers and twisted centralizers of the fixed grades subspaces and the norm functions that are widely used in the theory of spin groups. The presented groups are interesting for the study of generalized degenerate spin groups and for applications in computer science, physics, and engineering.