The kinetics of the interaction between Musashi-1 (MSI1) and RNA have been characterized using surface plasmon resonance biosensor analysis. Truncated variants of human MSI1 encompassing the two homologous RNA recognition motifs (RRM1 and RRM2) in tandem (aa 1-200), and the two RRMs in isolation (aa 1-103 and aa 104-200, respectively) were produced. The proteins were injected over sensor surfaces with immobilized RNA, varying in sequence and length, and with one or two RRM binding motifs. The interactions of the individual RRMs with all RNA variants were well described by a 1:1 interaction model. The interaction between the MSI1 variant encompassing both RRM motifs was bivalent and rapid for all RNA variants. Due to difficulties in fitting this complex data using standard procedures, we devised a new method to quantify the interactions. It revealed that two RRMs in tandem resulted in a significantly longer residence time than a single RRM. It also showed that RNA with double UAG binding motifs and potential hairpin structures forms less stable bivalent complexes with MSI1 than the single UAG motif containing linear RNA. Substituting the UAG binding motif with a CAG sequence resulted in a reduction of the affinity of the individual RRMs, but for MSI1, this reduction was strongly enhanced, demonstrating the importance of bivalency for specificity. This study has provided new insights into the interaction between MSI1 and RNA and an understanding of how individual domains contribute to the overall interaction. It provides an explanation for why many RNA-binding proteins contain dual RRMs.