<p>In recent years, quaternionic Fourier analysis has attracted increasing interest due to its potential application in signal analysis and image processing. This paper addresses the duality principle and biorthogonality relation on quaternionic Gabor systems. It is well known that the Ron–Shen duality principle and the Wexler–Raz biorthogonality relation play an important role in traditional Gabor analysis. We in this paper show that neither the Ron–Shen duality principle nor the traditional Wexler–Raz biorthogonality relation holds for quaternionic Gabor systems. And under the condition that the products of time-frequency shift parameters are rational numbers, we characterize the quaternionic Gabor Riesz sequences, present a sufficient condition on “<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10174_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {G}(g,\alpha ,\,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">G</mi> <mo stretchy="false">(</mo> <mi>g</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mspace width="0.166667em" /> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is a frame for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10174_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>,</mo> <mspace width="0.166667em" /> <mi mathvariant="double-struck">H</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10174_Article_IEq3.gif" Format="GIF" Height="6" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Leftrightarrow \)</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">⇔</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10174_Article_IEq4.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathcal {G}(g,\frac{1}{\beta },\,\frac{1}{\alpha })\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">G</mi> <mo stretchy="false">(</mo> <mi>g</mi> <mo>,</mo> <mfrac> <mn>1</mn> <mi>β</mi> </mfrac> <mo>,</mo> <mspace width="0.166667em" /> <mfrac> <mn>1</mn> <mi>α</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is a Riesz sequence in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10174_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>,</mo> <mspace width="0.166667em" /> <mi mathvariant="double-struck">H</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>", and establish a biorthogonality relation on quaternionic Gabor systems.</p>