In this Letter, the mathematical expressions corresponding to the kernel, local and global spin softness have been derived, and their relationship with other indices have been explored. Introducing various spin kernels, the mathematical framework of the spin polarized version of the chemical reactivity indices have been completed. Furthermore, new linear response functions have been defined and their relationship with the softness hierarchy are exposed. Finally, the importance of some of these indices has been illustrated for the reactivity pattern of open shell molecules. (c) 2005 Elsevier B.V. All rights reserved.