  We introduce a basic intuitionistic conditional logic $\mathsf{IntCK}$ that
we show to be complete both relative to a special type of Kripke models and
relative to a standard translation into first-order intuitionistic logic. We
show that $\mathsf{IntCK}$ stands in a very natural relation to other similar
logics, like the basic classical conditional logic $\mathsf{CK}$ and the basic
intuitionistic modal logic $\mathsf{IK}$. As for the basic intuitionistic
conditional logic $\mathsf{ICK}$ proposed by Y. Weiss, $\mathsf{IntCK}$ extends
its language with a diamond-like conditional modality, but its
diamond-conditional-free fragment is also a proper extension of $\mathsf{ICK}$.
We briefly discuss the resulting gap between the two candidate systems of basic
intuitionistic conditional logic and the possible pros and cons of both
candidates.
