The present invention relates to polyamide (A) and polyolefin (B) blends containing nanofillers in which thc polyamide forms the matrix. These blends can also be referred to as "polyamide (A), polyolefin (B) and nanofiller blends in which the polyamide fonns the matrix". The invention also relates to structures with barrier properties comprising at least one layer of these blends and optionally at least one layer of another material. These structures are a barrier to numerous fluids, and in particular in oxygen, to styrene, to furnigation fluids, to pentane and to air conditioning fluids. These structures can be made into bottles, reservoirs, containers, pipes and vessels of all sorts. They can also be converted to films which are used to make packagings.