I'm not certain that they are aphids, they could also be mealy bugs. Either way, they are a problem for your other house plants. There are insecticidal soap solutions you can buy from a garden store which are effective. Solutions that include pyrethrins are the best of all. Spray the plant carefully so that all the nooks and crannies in the buds are reached, especially on the underside of the leaves and where the leaves join to the stem.
Spray again in 2-3 days (the eggs of aphids are resistant and they will have a second hatching).
Check your other house plants carefully for any cross-infection, spray them too if necc.
John Doe wrote:
> How should I get rid of them? I guess for now I'll set the basil outside,
> however it will die out there if I leave it for too long. Your input is
> "Kim" <angelwings121NOSPAM at hotmail.com> wrote in message
> news:N9TK9.10830t6.10715 at nwrddc03.gnilink.net...> >
> > aphids.....big problem they'll get to ur plants and destroy them, they are
> > danger to all plants in your house