Multilayered polymer films are configured so that successive constituent layer packets can be delaminated in continuous sheet form from the remaining film. The new films are compatible with known coextrusion manufacturing techniques, and can also be made without the use of adhesive layers between layer packets that are tailored to be individually peelable from the remainder of the film. Instead, combinations of polymer compositions are used to allow non-adhesive polymer layers to be combined in such a way that delamination of the film is likely to occur along a plurality of delamination surfaces corresponding to interfaces between particular pairs of layers for which the peel strength is reduced relative to the peel strength at other layer interfaces within the film. The absence of an adhesive between peelable layer packets results in the delamination being irreversible.