In this paper we initiate an investigation into the class of meet semilattices endowed with endomorphism. A consideration subdirectly irreducible algebras leads to a description subclass those (S;∧,k)(S;∧,k) in which (S;∧)(S;∧) is semilattice and kk endomorphism on SS characterised by property k⩾idSk⩾idS. We particularly show that such algebra if only it chain one following forms ⋯<aj&am...