Halogen-free flame retardant polymer compositions are made from an ABS resin as the sole resin, and a P, P'-dihydrocarbyl pentaerythrityl diphosphonate in which the total number of carbon atoms in the two hydrocarbyl substituents is 8 or less as the sole phosphorus-containing flame retardant, or form at least one thermoplastic polymer and a combination of at least one of the foregoing P, P'-dihydrocarbyl pentaerythrityl disphosphonates, and at least one arylbis (dihydrocarbylphosphate) and/or at least one arylbis (dihydrocarbylphosphinate). Effective flame retardancy (UL-94 V-0) is achieved without material disruption of physical property requirements of the substrate polymer.