RNA targeting is an evolving new approach to anticancer therapeutics that requires identification of small molecules to selectively target specific RNA structures. In this report, the interaction of biogenic polyamines spermine, spermidine and the synthetic analogue 1-naphthylacetyl spermine with three double-stranded RNA polynucleotides--poly(I)·poly(C), poly(C)·poly(G), and poly(A)·poly(U)--has been described to understand the structural and thermodynamic basis of the binding and the comparative efficacy of the analogue over the natural polyamines. Circular dichroism spectroscopy, thermal melting experiments, and ethidium bromide displacement assay were used to characterize the interaction. Microcalorimetry studies were performed to deduce the energetics of the interaction and atomic force microscopy experiments done to gain insight into the interaction at the molecular level. The experiments demonstrated structural perturbations in the polynucleotides on binding of the polyamines. Thermal melting studies showed enhanced stabilization of RNA-polyamine complexes with increase in the total standard molar enthalpy of transition. The binding affinity was strongest for poly(I)·poly(C) as revealed by microcalorimetry results and varied as poly(I)·poly(C) > poly(C)·poly(G) > poly(A)·poly(U). The order of affinity for the polyamines was spermine >1-naphthylacetyl spermine > spermidine. Total enthalpy-entropy compensation and high standard molar heat capacity values characterized the interactions. The results of the study on the binding of polyamines to dsRNAs presented here have been compared to those reported earlier with dsDNAs. The present findings advance our knowledge on the mechanism of interaction of polyamines with RNA and may help in the search for analogues that can interfere with biogenic polyamine metabolism and function.