We introduce the parameter of block elimination distance as a measure how close graph is to some particular class. Formally, given class $${\mathcal {G}}$$ , {B}}({\mathcal {G}})$$ contains all graphs whose blocks belong and {A}}({\mathcal where removal vertex creates in . Given hereditary we recursively define $${{\mathcal {G}}}^{(k)}$$ so that {G}}^{(0)}={\mathcal and, if $$k\ge 1$$ {G}}^{(k)...