We study basic properties of monomial ideals with linear quotients. It is shown that if the monomial ideal I has linear quotients, then the squarefree part of I and each component of I as well as have linear quotients, where is the graded maximal ideal of the polynomial ring. As an analogy to the Rearrangement Lemma of Björner and Wachs we also show that for a monomial ideal with linear quotients the admissible order of the generators can be chosen degree increasingly
