Stability analysis of some networks with interacting servers Rosario Delgado 1 and Evsey Morozov 2 1 Corresponding author Departament de Matem` atiques. Universitat Aut` onoma de Barcelona. Edifici C- Campus de la UAB. 08193 Bellaterra (Cerdanyola del Vall` es)- Barcelona, Spain. delgado@mat.uab.cat Supported by the project MEC ref. MTM2012-33937 and ERDF (European Regional Development Found) “A way to build Europe”. 2 Institute of Applied Mathematical Research, Russian Academy of Sciences and Petrozavodsk State University, Russia. emorozov@karelia.ru Supported by the Program of strategic development of Petrozavodsk State University for 2012-2016. Abstract. In this work, the fluid limit approach is applied to find sta- bility conditions of two models of queueing networks with interacting servers. We first consider a two-station queueing model with two cus- tomer classes in which customers that are awaiting service at any queue can move to the other station, whenever it is free, to be served there immediately. Then we consider a cascade-type three-station system in which the third station, whenever it is free, can assist the other two sta- tions. In both models, each station is fed by a renewal input with general i.i.d. inter-arrival times and general i.i.d. service times. keywords: cascade networks, fluid limit approach, interacting servers, stability, X-model. 1 Introduction In the present paper, we study two variants of the cascade networks considered in [12]. First, we consider a queueing system consisting of two basic customer classes, 1 and 2, and two servers. Class-j customers are primarily assigned to server j, j =1, 2. However, servers are cross-trained so that, when become free, they can serve customers from the other class (that is, from the queue of other server). Such a model, which is called X-model in [19], differs from the two- station cascade network considered in [12] in which in that paper, the 1st server, being free, cannot support the 2nd one. Motivation for the study of these models can be found in [19]. Secondly, we study a generalized cascade model consisting of three stations with three basic customer classes, in which the 3rd station assists the 2nd station which, in turn, assists the 1st one, as was the case of the