This is the second volume of the Belov/Karasik/Rowen/Vishne book on the Computational Aspects of Polynomial Idenities . This volume will begin with the characteristic p version of Specht's conjecture for affine PI-algebras. The remainder of volume II is concerend with related versions of specht's conjecture including algebras with involution and non associative algebras including altrernative algebras, Jordan algebras and Lie algebras.