Social bonds can be a way for individuals to gain access to crucial resources and services that cannot be taken by force and are therefore subject to leverage. Bonds between the sexes can provide access to services that are specific to the other sex. Females exert leverage over males in terms of mating access, males have leverage over females in terms of the service protection, and both sexes exert leverage over the other sex in terms of tolerance and agonistic support. While mating access can be coerced in some circumstances, most services cannot be forced. Here, we use theoretical considerations to explore when sources of leverage over the opposite sex lead to between-sex bonds. Focussing on primates living in multi-male multi-female groups, we predict that leverage over the other sex will be higher, when 1) the receiver benefits on average more than the provider, 2) receivers cannot share the resource, and 3) the resource is rare and valuable. If these conditions are fulfilled, and given the mutual nature of a social bond, we expect bonds to be found, 4) when long-term targeting of the same partner yields benefits. We argue that a female's main source of leverage is mating access, whereas males mainly exert leverage over females in terms of protection of females and offspring. The combination of female mate choice with male protection and care for young is expected to promote between-sex bonds; reduced female cohesion and/or secondary female dispersal are expected to further increase the strength of between-sex bonds. The investment in shared offspring results in interdependency between male and female strategies, but the different services provided by females and males indicate that affiliative exchanges associated with bonds between the sexes will be typically asymmetric and vary over time. Thus, bonds between the sexes are expected to form in a limited number of circumstances where both sexes have leverage over the other sex in terms of their respective sex-specific services. While a systematic test of this proposal is hampered by the dearth of data on species lacking social bonds between the sexes, the data currently available are consistent with our hypothesis.