A continuum $X$ has unique cone provided that the following property holds: if $Y$ is a continuum and $\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{e}(X)$ is homeomorphic to $\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{e}(Y)$, then $X$ is homeomorphic to $Y$. In this talk we consider the problem of the uniqueness of cones for some not locally connected continua, e.g. the indecomposable continua and the compactifications of the ray.