<p>We study the viscoelastic pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity <Equation ID="Equ64"> <EquationSource Format="TEX">\(\begin{aligned} u_t-M(\left\| \nabla u\right\| ^2)\Delta u -\alpha \Delta u_t+\int _{0}^{t}h(t-s)\Delta u(s){\textrm{d}}s=\vert u\vert ^{p-2}u\ln \vert u\vert \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <msub> <mi>u</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>M</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mfenced close="∥" open="∥"> <mi mathvariant="normal">∇</mi> <mi>u</mi> </mfenced> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> <mi mathvariant="normal">Δ</mi> <mi>u</mi> <mo>-</mo> <mi>α</mi> <mi mathvariant="normal">Δ</mi> <msub> <mi>u</mi> <mi>t</mi> </msub> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mi>t</mi> </msubsup> <mi>h</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>-</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mi mathvariant="normal">Δ</mi> <mi>u</mi> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mtext>d</mtext> <mi>s</mi> <mo>=</mo> <msup> <mrow> <mo stretchy="false">|</mo> <mi>u</mi> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>p</mi> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mi>u</mi> <mo>ln</mo> <mrow> <mo stretchy="false">|</mo> <mi>u</mi> <mo stretchy="false">|</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>and examine the effects of the viscoelastic term and the logarithmic nonlinearity on the asymptotic behavior of its weak solutions.</p>