Measles virus belongs to the Paramyxoviridae family within the Mononegavirales order. Its non-segmented, single stranded, negative sense RNA genome is encapsidated by the nucleoprotein (N) to form a helical nucleocapsid. This ribonucleoproteic complex is the substrate for both transcription and replication. The RNA-dependent RNA polymerase binds to the nucleocapsid template via its co-factor, the phosphoprotein (P). In this review, we summarize the main experimental data pointing out the abundance of structural disorder within measles virus N and P. We also describe studies indicating that structural disorder is a widespread property in the replicative complex of Paramyxoviridae and, more generally, of Mononegavirales. The functional implications of structural disorder are also discussed. Finally, we propose a model where the flexibility of the disordered N and P domains allows the formation of a tripartite complex (N degrees-P-L) during replication, followed by the delivery of N monomers to the newly synthesized genomic RNA chain.