In various tunnel-junction arrays having two conducting branches between the source and the drain electrodes, a new type of Coulomb blockade gap and Coulomb staircase are observed. We attribute their appearance to the topology of the arrays which induces multiple electrons to become trapped. When the number of trapped electrons is varied by external sources, the current may flow during the transition, leading to an additional Coulomb blockade gap or Coulomb staircase in the I-V characteristics. The tunneling processes which lead to the formation and destruction of the additional gap and staircase are analyzed. (C) 1999 Academic Press.