I've had them reseed but after a couple of years they seem to stop and I need to buy some new plants.

There are yellow flowering Alyssum: Aurinia Saxatilis, maybe also called "Basket of Gold", Gold Dust" and Madwort that are perennials.

The common white Sweet Alyssum is listed as a hardy annual. But it self seeds quite freely. When I lift and discard the old dead plants in the spring, I can generally count on a carpet of new seedlings underneath. I'll buy new plants every few years though, too.

Thanks for the replies.

Well, this is actually good news, as I always hated the way the dead alyssum looked before the new growth took over. Now I can just remove 'em when they get ugly.

Happy gardening.

-Ray

Duluthinblooms4 gave very good information about alyssum...
i would also add that during the summer....you can cut back the older growth about a third of the way down the
plants and wait a couple weeks to have revived blooms...

carol