Zika virus (ZIKV) has emerged as a pathogen of major health concern. The virus relies on its non-structural protein 5 (NS5) including a methyl-transferase (MTase) and a RNA-dependent RNA polymerase (RdRp) for capping and synthesis of the viral RNA and the nonstructural protein 3 (NS3) with its protease and helicase domain for polyprotein possessing, unwinding dsRNA proceeding replication, and NTPase/RTPase activities. In this study we present for the first time insights into the overall structure of the entire French Polynesia ZIKV NS3 in solution. The protein is elongated and flexible in solution. Solution studies of the individual protease- and helicase domains show the compactness of the two monomeric enzymes as well as the contribution of the 10-residues linker region to the flexibility of the entire NS3. We show also the solution X-ray scattering data of the French Polynesia ZIKV NS5, which is dimeric in solution and switches to oligomers in a concentration-dependent manner. The solution shapes of the MTase and RdRp domains are described. The dimer arrangement of ZIKV NS5 is discussed in terms of its importance for MTase-RdRp communication and concerted interaction with its flexible and monomeric counterpart NS3 during viral replication and capping. The comparison of ZIKV NS3 and -NS5 solution data with the related DENV nonstructural proteins shed light into the similarities and diversities of these classes of enzymes. Finally, the effect of ATPase inhibitors to the enzymatic active ZIKV NS3 and the individual helicase are provided.