The invention relates to adhesive compositions having a modified polyethylene; an unmodified polyethylene of a certain density and a styrene-based elastomer. The styrene-based elastomer is present in a weight percentage of 10 to 45 wt. percent relative to the total weight of the elastomer plus the modified and unmodified polyethylenes. The adhesive composition is particularly useful in multilayer composite structures having polypropylene as one substrate and having bonded thereto a polyethylene or a layer which is made from an ethylene copolmer such as an ethylene/acid copolymer or an ethylene acid ionomer. In addition, the adhesive composition is particularly useful in multilayer structures having five layers wherein a single adhesive composition is needed as layer two and four and the other structural layers are, for example, polyethylene/nylon/polypropylene or similar structures which would heretofore require two different polyolefin base adhesives.