Title: Stability islands in domains of separatrix crossings in slow-fast Hamiltonian systems Author: A.Neishtadt (1), C. Sim\'o (2), D. Treschev (3) and A. Vasiliev (1) (1) Space Research Institute, Profsoyuznaya 84/32, Moscow 117997, Russia. (2) Dept. de Matem\`atica Aplicada i An\`alisi, Univ. de Barcelona, Gran Via, 585, Barcelona 08007, Spain. (3) V.A. Steklov Mathematical Institute, Gubkina 8, Moscow 119991, Russia. E-mail: aneishta@iki.rssi.ru, carles@maia.ub.es, valex@iki.rssi.ru, treschev@mi.ras.ru Abstract We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of time derivatives of slow and fast variables is of order 0