There is provided a series of novel substituted gamma-lactams of Formula (I) ##STR00001## wherein R.sup.1, R.sup.2, R.sup.3, R.sup.4 and R.sup.5 are defined herein, their pharmaceutical compositions and methods of use. These novel compounds inhibit the processing of amyloid precursor protein (APP) by .beta.-secretase and, more specifically, inhibit the production of A.beta.-peptide. The present invention is directed to compounds useful in the treatment of neurological disorders related to .beta.-amyloid production, such as Alzheimer's disease and other conditions affected by anti-amyloid activity.