The structure and thermal properties of linear low density polyethylene (LLDPE)/medium soft paraffin wax blends, prepared by melt mixing, were investigated by differential scanning calorimetry (DSC) and small- and wide-angle X-ray scattering (SAXS and WAXS). The blends form a single phase in the melt as determined by SAXS. Upon cooling from the melt, two crystalline phases develop for blends with more than 10 wt % wax characterized by widely different melting points. The wax acts as an effective plasticizer for LLDPE, decreasing both its crystallization and melting temperature. The higher melting point crystalline phase is formed by less branched LLDPE fractions. On the other hand, the lower melting point crystalline phase is a wax-rich phase constituted by cocrystals of extended chain wax and short linear sequences of highly branched LLDPE chains. The presence of cocrystals was evidenced by standard DSC results, successive self-nucleation and annealing (SSA) thermal fractionation and by the detection of a new SAXS signal attributed to the lamellar long period of the cocrystals. ; The POLYMAT/UPV/EHU team would like to acknowledge funding from the following projects: “UPV/EHU Infrastructure: INF 14/38”; “Mineco/FEDER: SINF 130I001726XV1/Ref: UNPV13–4E–1726”; and “Mineco MAT2014-53437-C2-P”. Financial support from the Projects MAT2012-31088 (SpanishMINECO and EU) and IT-654-13 (Basque Government) is acknowledged by CFM team. The National Research Foundation South Africa is also acknowledged for financial support of the project. R.A.P.-C gratefully acknowledges the award of a PhD fellowship by POLYMAT Basque Center for Macromolecular Design and Engineering (BERC BOVP N8134).