Pseudo-MTL algebras or weak pseudo-BL algebras are non-commutative fuzzy structures which arise from pseudo-t-norms, namely, pseudo-BL algebras without the pseudo-divisibility condition. The aim of this paper is to investigate the properties of pseudo-BL algebras that also hold for pseudo-MTL algebras. We will also study some classes of pseudo-MTL algebras such as good, local and Archimedean pseudo-MTL algebras and we show that, generally, an Archimedean pseudo-MTL algebra is not commutative. We prove that any locally finite pseudo-MTL algebra is Archimedean.