The present invention relates to a polymer composition comprising (A) from 60 to 90 wt % of a non-elastomeric polyethylene; (B) from 9.0 to 38 wt % of an elastomer; wherein onto component (A) or components (A) and (B) an acid grafting agent (C) has been grafted in an amount of from 0.01 to 3.0 wt %, all based on the total weight of the polymer composition, and wherein the polymer composition has two distinct peaks and a valley between said peaks in the GPC curve and a Z value, determined from the areas below the two peaks of the GPC curve, of at least −0.3, wherein the Z-value is determined according to formula (I) Z=s/Abs(B−A) (I) wherein Abs(B−A) is the absolute value of (B−A); A=the area, between the tangent parallel to the MW axis going through log M (Min) and the LS15 signal, from log M of 5.1 to log M value where the LS signal is minimum log M (Min), in the log M range between 5.1 and 6; B=the area, between the tangent parallel to the MW axis going through log M (Min) and the LS 15 signal, from log M(Min) to the point where the LS signal is crossed again; and s is the slope between the two peaks of the GPC curve, defined at log M of 5.1 and 6, wherein the GPC curve is defined as the concentration normalized LS 15 signal along the molecular weight of conventional GPC, obtained from the GPC-VISC-LS analysis, a multi-layer structure such as a coated metal pipe, comprising one layer comprising said polymer composition and the use of said polymer composition as adhesive polymer composition and for the production of a multi-layer structure.