The invention provides 4-amino-4-oxobutanoyl peptide compounds of Formula I and the pharmaceutically salts and hydrates thereof. The variables R1-R9, R16, R18, R19, n, M, n, M, and Z are defined herein. Certain compounds of Formula I are useful as antiviral agents. Certain 4-amino-4-oxobutanoyl peptide compounds disclosed herein are potent and/or selective inhibitors of viral replication, particularly Hepatitis C virus replication. The invention also provides pharmaceutical compositions containing one or more 4-amino-4-oxobutanoyl peptide compounds and one or more pharmaceutically acceptable carriers. Such pharmaceutical compositions may contain 4-amino-4-oxobutanoyl peptide compound as the only active agent or may contain a combination of 4-amino-4-oxobutanoyl peptide containing peptides compound and one or more other pharmaceutically active agents. The invention also provides methods for treating viral infections, including Hepatitis C infections, in mammals.