Let $𝒟$ be the system of all distributive lattices and let ${𝒟}_0$ be the system of all $L\in 𝒟$ such that $L$ possesses the least element. Further, let ${𝒟}_1$ be the system of all infinitely distributive lattices belonging to ${𝒟}_0$. In the present paper we investigate the radical classes of the systems $𝒟$, ${𝒟}_0$ and ${𝒟}_1$.