The present invention relates to a stable blended diesel fuel comprising an olefinic diesel fuel blending stock. The olefinic diesel fuel blending stock of the invention comprises olefins in an amount of 2 to 80 weight percent, non-olefins in an amount of 20 to 98 weight percent wherein the non-olefins are substantially comprised of paraffins, oxygenates in an amount of at least 0.012 weight percent and sulfur in an amount of less than 1 ppm. To provide acceptable stability, the blended diesel fuel comprising the olefinic diesel fuel blending stock comprises a sulfur-free antioxidant. The blended diesel fuel comprising the olefinic diesel fuel blending stock and sulfur-free antioxidant added has a peroxide content of less than 5 ppm when stored at 60.degree. C. for 4 weeks. The present invention also relates to processes for making the stable blended diesel fuel and olefinic diesel fuel blending stocks as defined above.