Intuitionistic conditional logic, studied by Weiss, Ciardelli and Liu, and Olkhovikov, aims at providing a constructive analysis of conditional reasoning. In this framework, the would and the might conditional operators are no longer interdefinable. The intuitionistic conditional logics considered in the literature are defined by setting Chellas’ conditional logic CK, whose semantics is defined using selection functions, within the constructive and intuitionistic framework introduced for intuitionistic modal logics. This operation gives rise to a constructive variant of might-free-CK, which we call The image is a mathematical notation depicting a logical derivation. It includes Greek letters and logical symbols. The formula is structured as follows: - Top row: D_1 quad D_2 quad D_3 quad D_4 quad D_5 quad D_6 quad D_7 quad D_8 quad D_9 - Second row: varphi supset rho quad rho supset psi quad varphi supset psi quad eta supset xi quad xi supset eta quad xi supset varphi quad eta supset varphi quad sigma land psi supset chi land psi quad sigma land chi supset - Third row: Gamma, Gamma', rho land sigma, xi land chi, varphi land psi supset The notation uses logical symbols such as supset (implies), land (and), and Greek letters varphi, rho, psi, eta, xi, sigma, chi., and an intuitionistic variant of CK, called IntCK. Building on the proof systems defined for CK and for intuitionistic modal logics, in this paper we introduce a nested calculus for IntCK and a sequent calculus for Text "ConstCK" followed by a square with an arrow pointing to the right, resembling a symbolic representation or logo.. Based on the sequent calculus, we define ConstCK, a conservative extension of Weiss’ logic The image shows the text "ConstCK" followed by a right-pointing arrow symbol enclosed in a square.with the might operator. We introduce a class of models and an axiomatisation for ConstCK, and extend these result to some extensions of ConstCK.