Leeks, like garlic and onions, belong to a vegetable family called the Allium vegetables. Since leeks are related to garlic and onions, they contain many of the same beneficial compounds found in these well-researched, health-promoting vegetables.t's important to remember that even in the absence of research studies to confirm health benefits, leeks still belong to the same allium vegetable family as onions and garlic and contain many health-supportive substances that are similar to (or identical with) the substances in their fellow allium vegetables.