In this chapter, we will inquire into some non-contractive and or non-monotonic logics that can be found in the literature. Our starting point, as in the previous chapters, will be subtracting some structural rules from \(\mathbf {LK}\) , in this case Contraction and/or Weakening. But unlike previous chapters, here we will move away from the Strong Kleene family of logics and present some other logics of different nature. We begin by introducing Classical Linear Logic, \(\mathbb {CLL}\) , a logic that is sometimes presented as Classical Logic with devices to control Weakening and Contraction along the proofs. This logic will occupy most of the chapter. We will start by showing some syntactic features of its language, then we will introduce phase semantics, and finally study some of its metainferential properties. Then we will move to logics where either Weakening or Contraction fails (but not both). We proceed in the following order: first, we begin with some logics that drop Contraction but retain Weakening. In particular, we will study a way to characterize the family of finitely many-valued logics of Łukasiewicz by adding some axioms and bounded Contraction to Affine Linear Logic (a system that is obtained from the calculus \(\mathbf {CLL}\) plus Weakening). We will also survey a non-contractive presentation of \(\mathbf {LK}\) , a logic that has the same admissible rules as \(\mathbf {LK}\) . And finally, we will make the opposite move, and we will present \(\mathbb {LKNW}\) , a logic that is obtained from taking the additive fragment of \(\mathbf {CLL}\) and adding Contraction.