Abstract. A {\it cutset} of a poset is a subset which meets every maximal chain, and a {\it fibre} is a subset which meets every maximal antichain. The questions we address are: {\it When is every minimal cutset an antichain?} and the analogous {\it When is every minimal fibre a chain?} For finite posets, Lonc and Rival showed that the answer to both questions is precisely {\it when the poset is fence-free}. We extend this result to classes of infinite posets satisfying certain chain conditions.

AMS Subject Classification (1991): 06A07

Received October 27, 1993 and in revised form March 11, 1994. (Registered under 5592/2009.)