Actually, @Kardamom , you should read the wikipedia entry. It is entirely possible for asexual people to be attracted to one or the other.
The more you know! [sing-song]
http://en.wikipedia.org/wiki/Asexuality
Asexuality is distinct from abstention from sexual activity and from celibacy, which are behavioral; the latter is usually for a religious reason.[9] A sexual orientation, unlike a behavior, is believed to be “enduring”.[10][11] Some asexuals do have sex, despite lacking a desire for it.[12]
Asexuals, while typically lacking in sexual desire for either sex, may engage in purely emotional romantic relationships.[20][21][22] Terms concerning this:
aromantic: lack of romantic attraction towards anyone of any gender
biromantic: romantic attraction towards person(s) of either gender
heteroromantic: romantic attraction towards person(s) of the opposite gender
homoromantic: romantic attraction towards person(s) of the same gender
panromantic: romantic attraction towards person(s) of any gender or lack of gender
transromantic: romantic attraction towards person(s) of variant or ambiguous gender
polyromantic: romantic attraction towards person(s) of more than one gender or sex but without implying, as biromantic does, that there are only two genders or sexes
The word “attraction” does not refer to sex, only.