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1.
A romantic attraction to a member of the opposite sex, can include sexual attraction or not.

In the case of asexuals, heteromantic would mean they have romantic feelings towards the opposite sex, but not any sexual desire.

The desire for a romantic relationship with someone of the opposite sex
I am physically attracted to both males and females, but am only really interested in dating males. So I am bisexual but heteromantic.
by MALM May 04, 2012