Let ϒ be a generalised cone in Rd. Roughly speaking, Yaglom limit describes the behaviour of the process conditioned not to exit the cone, or, in other words, not to become extinct or not to be absorbed. In the talk we will discuss the existence of this limit for a class of (not necessarily symmetric) α-stable Lévy processes living in the cone ϒ. To this end, we will use the so-called Martin kernel at inifinty - the invariant function for the killed semigroup - to obtain the so-called entrance law from the origin, which we also call the self-similar solution. Using this approach, for the isotropic case we will also obtain the large-time asymptotics for the killed semigroup and provide several examples of our resutts.