When antibodies raised in response to a particular pathogen bind with immunologically similar pathogens it may facilitate infection through a phenomenon known as antibody-dependent enhancement (ADE). This process occurs between the four serotypes of dengue virus and, furthermore, secondary infection is a major risk factor in dengue hemorrhagic fever (DHF). Theory has suggested that ADE may be responsible for the large immunological distance between dengue serotypes. We investigate this hypothesis using an epidemic model for dengue in which immunological distance and the strength of immune cross-reaction are expressed separately. Cross-enhancement is considered in three alternative forms acting on susceptibility, transmission and mortality. Previous models have shown that transmission and mortality enhancement can lead to periodicity or chaos. We confirm this result for reasonable levels of susceptibility and transmission enhancement but not for mortality enhancement. We also show that when the two strains have identical basic reproductive numbers no form of enhancement leads to competitive exclusion. When the two strains have different basic reproductive numbers susceptibility or transmission enhancement allow strains with greater immunological similarity to stably coexist but mortality enhancement forces strains to be more distinct. All three forms of enhancement can be associated with DHF and we conclude that mortality enhancement must be dominant if ADE really is responsible for the immunological distance between dengue serotypes.