The invention provides novel .beta.-lactamase inhibitors, which are structurally unrelated to the natural product and semi-synthetic .beta.-lactamase inhibitors presently available, and which do not possess a .beta.-lactam pharmacophore. These new inhibitors are fully synthetic, allowing ready access to a wide variety of structurally related analogs. Certain embodiments of these new inhibitors also bind bacterial DD-peptidases, thus potentially acting both as .beta.-lactamase inhibitors and as antibiotics.