Let H denote a simply-connected cata-condensed polyhex. It is shown that if H has three hexagons in a row it does not have a maximum number of Kekulé structures. Otherwise, its number of Kekulé structures is equal to its number of sets of disjoint hexagons (including the empty set). These results lead to an efficient algorithm to determine simply-connected cata-condensed polyhexes with a maximum number of Kekulé structures. A table of such values for H with up to 100 hexagons is provided.