  We introduce two classes of $(p,q)$-It\^o--Hermite polynomials, the
post-quantum analogs of the $q$-It\^o--Hermite polynomials introduced recently
by Ismail and Zhang. We study their basic properties such as their operational
formulas of Rodrigues type, the corresponding raising and lowering operators as
well as their generating functions and the $(p,p$-differential equations they
obey.
