Let X be a degree d curve in the projective space P^r. A general hyperplane H intersects X at d distinct points; varying H defines a monodromy action on X∩H. The resulting permutation group G is the sectional monodromy group of X. When the ground field has characteristic zero the group G is known to be the full symmetric group.By work of Harris, if G contains the alternating group, then X satisfies a strengthened Castelnuovo's inequality (relating the degree and the genus of X).The talk is concerned with sectional monodromy groups in positive characteristic. I will describe all nonstrange nondegenerate curves in projective spaces of dimension r>2. for which G is not symmetric or alternating. For a particular family of plane curves. I will compute the sectional monodromy groups and thus answer an old question on Galois groups of generic trinomials.