Weak-base amphiphilic delivery peptide compositions are described for use in delivering large polar substances (cargo) into the cytosol of animal cells via an indirect endocytosis-mediated delivery process. The delivery peptides, which are predominantly non-ionic at neutral pH, bind but do not permeabilize cell membranes. After endocytosis of both delivery peptides and cargo, acidification of the endosome converts the delivery peptides to their polycationic form, whereupon they permeabilize the endosomal membrane and allow co-endocytosed cargo to pass from the endosome to the cytosol of the cell.