Similar　to　the　horizontal-to-vertical　Fourier　spectral　ratio　(HVF)　of　ground　motions,　the　horizontal-to-vertical　response　spectral　ratio　(HVR)　is　a　valuable　tool　for　evaluating　site　effects.　Although　these　two　spectral　ratios　often　exhibit　similar　behaviours,　each　possesses　its　own　set　of　properties,　prompting　increased　attention　to　their　relationship.　Previously,　the　relationship　between　HVF　and　HVR　has　been　statistically　investigated　to　explore　which　is　more　reasonable　for　predominant　period　estimation.　However,　the　theoretical　link　between　them　remains　unexplored.　To　clarify　their　theoretical　relationship,　in　this　study,　an　expression　relating　HVR　to　HVF　based　on　random　vibration　theory　was　derived.　The　accuracy　of　the　derived　expression　was　confirmed　through　a　comparison　with　the　results　obtained　via　direct　numerical　integration　using　real　seismic　records.　Subsequently,　based　on　the　derived　expression,　the　theoretical　relationship　between　HVF　and　HVR　was　systematically　explored.　HVR　was　found　to　be　the　result　of　smoothing　the　square　of　the　HVF,　and　the　spectral　window　for　this　smoothing　operation　was　determined　using　the　Fourier　amplitude　spectrum　of　the　vertical　ground　motion　and　the　oscillator　transfer　function.