We give a generalisation of Deligne-Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a nonarchimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties to unramified maximal tori inside Borel subgroups. In this paper we associate a family of so-called extended Deligne-Lusztig varieties to all tamely ramified maximal tori of the group.Moreover, we analyse the structure of various generalised Deligne-Lusztig varieties, and show that the "unramified" varieties, including a certain natural generalisation, do not produce all the irreducible representations in general. On the other hand, we prove results which together with some computations of Lusztig show that for SL 2 (Fq[[̟]]/(̟ 2 )), with odd q, the extended Deligne-Lusztig varieties do indeed afford all the irreducible representations.