Linear polydihalophosphazene polymers which are substantially free of gel are prepared by thermally polymerizing a cyclic polyhalophosphazene represented by the formula (NPX.sub.2).sub.3, wherein X is fluorine, chlorine or bromine in the presence of a catalyst which comprises the reaction product of a boron trihalide compound with an oxygenated phosphorus compound.In addition to producing substantially gel free polymers, the catalyst composition of the process of the invention permits improved control of molecular weight, lower polymerization temperature, high rates of conversion of (NPCl.sub.2).sub.3 to (NPCl.sub.2).sub.n and provides for more readily processible and derivatizable polymers.