A compound comprising an internally cross-linked amino acid sequence having the formula: or a pharmaceutically acceptable salt thereof, wherein: each R 1 and R 2 is independently H, alkyl, alkenyl, alkynyl, arylalkyl, cycloalkylalkyl, heteroarylalkyl, or heterocyclylalkyl, any of which is substituted or unsubstituted; each R 3 is independently alkylene, alkenylene, or alkynylene, any of which is substituted or unsubstituted; each x is independently 2, 3, or 6; each w and y is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20; z is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and each Xaa is independently an amino acid; wherein the cross-linked amino acid sequence is at least 80% identical to an amino acid sequence selected from the group consisting of: SEQ ID NOs: 1-4; wherein the cross-linked amino acid sequence has an alpha-helical conformation; or having at least 18 contiguous amino acids of SEQ ID NOs: 1-4, wherein the side chains of one or two pairs of amino acids separated by 2, 3 or 6 amino acids are replaced, relative to the corresponding parent non-internally cross linked AMP by the linking group R 3, having 1, 2, 3, 4 or 5 amino acid substitutions, wherein the substitutions are one or more of: (i) a substitution with a basic amino acid, (ii) a substitution with a lysine, (iii) a substitution with a histidine, (iv) a substitution with a D-alanine, and (v) a substitution with an alanine; and wherein the compound exhibits an antimicrobial effect against at least one bacterium; and wherein the compound is selectively lytic/cytotoxic to bacteria and not to mammalian membrane. having the formula: or a pharmaceutically acceptable salt thereof, wherein: each R 1 and R 2 is independently H, alkyl, alkenyl, alkynyl, arylalkyl, cycloalkylalkyl, heteroarylalkyl, or heterocyclylalkyl, any of which is substituted or unsubstituted; each R 3 is independently alkylene, alkenylene, or alkynylene, any of which is substituted or unsubstituted; each x is independently 2, 3, or 6; each w and y is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20; z is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and each Xaa is independently an amino acid; wherein the cross-linked amino acid sequence is at least 80% identical to an amino acid sequence selected from the group consisting of: SEQ ID NOs: 1-4; wherein the cross-linked amino acid sequence has an alpha-helical conformation; or or a pharmaceutically acceptable salt thereof, wherein: each R 1 and R 2 is independently H, alkyl, alkenyl, alkynyl, arylalkyl, cycloalkylalkyl, heteroarylalkyl, or heterocyclylalkyl, any of which is substituted or unsubstituted; each R 3 is independently alkylene, alkenylene, or alkynylene, any of which is substituted or unsubstituted; each x is independently 2, 3, or 6; each w and y is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20; z is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and each Xaa is independently an amino acid; wherein the cross-linked amino acid sequence is at least 80% identical to an amino acid sequence selected from the group consisting of: SEQ ID NOs: 1-4; wherein the cross-linked amino acid sequence has an alpha-helical conformation; or each R 1 and R 2 is independently H, alkyl, alkenyl, alkynyl, arylalkyl, cycloalkylalkyl, heteroarylalkyl, or heterocyclylalkyl, any of which is substituted or unsubstituted; each R 3 is independently alkylene, alkenylene, or alkynylene, any of which is substituted or unsubstituted; each x is independently 2, 3, or 6; each w and y is independently 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20; z is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10; and each Xaa is independently an amino acid; wherein the cross-linked amino acid sequence is at least 80% identical to an amino acid sequence selected from the group consisting of: SEQ ID NOs: 1-4; wherein the cross-linked amino acid sequence has an alpha-helical conformation; or having at least 18 contiguous amino acids of SEQ ID NOs: 1-4, wherein the side chains of one or two pairs of amino acids separated by 2, 3 or 6 amino acids are replaced, relative to the corresponding parent non-internally cross linked AMP by the linking group R 3, having 1, 2, 3, 4 or 5 amino acid substitutions, wherein the substitutions are one or more of: (i) a substitution with a basic amino acid, (ii) a substitution with a lysine, (iii) a substitution with a histidine, (iv) a substitution with a D-alanine, and (v) a substitution with an alanine; and wherein the side chains of one or two pairs of amino acids separated by 2, 3 or 6 amino acids are replaced, relative to the corresponding parent non-internally cross linked AMP by the linking group R 3, having 1, 2, 3, 4 or 5 amino acid substitutions, wherein the substitutions are one or more of: (i) a substitution with a basic amino acid, (ii) a substitution with a lysine, (iii) a substitution with a histidine, (iv) a substitution with a D-alanine, and (v) a substitution with an alanine; and wherein the compound exhibits an antimicrobial effect against at least one bacterium; and wherein the compound is selectively lytic/cytotoxic to bacteria and not to mammalian membrane.