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We obtain a Liouville comparison principle for entire weak solutions ( u , v ) of quasilinear singular parabolic second-order partial differential inequalities of the formu  t   -  A   (  u  )   -    |  u  |    q  -  1    u  ≥   v  t   -  A   (  v  )   -    |  v  |    q  -  1    v    ${ u_t - A(u)-|u|^{q-1}u \ge v_t - A (v)-|v|^{q-1}v }$    on the set  τ   =   (  τ  ,  +  ∞  )   ×    ℝ   n${{\mathbb {S}}_{\tau }= (\tau , +\infty )\times {\mathbb {R}}^n}$   , where  q  &gt; 0,  n  ≥ 1, τ is a real number orτ  =  -  ∞    ${\tau =-\infty }$   , and the differential operator  A  satisfies the α-monotonicity condition. Model examples of the operator  A  in our study are the well-known  p -Laplacian operator defined by the relationΔ  p    (  w  )   =   div  x    (  |    ∇  x   w    |   p  -  2∇  x   w  )${\Delta _p (w)=\operatorname{div}_x(|\nabla _x w|^{p-2}\nabla _x w) }$    and its well-known modification defined byΔ  ˜   p    (  w  )   =   ∑   i  =  1   n    ∂   ∂   x  i(  |∂  w    ∂   x  i|   p  -  2∂  w    ∂   x  i)${ \widetilde{\Delta }_p (w) = \sum _{i=1}^n\frac{\partial }{\partial x_i}( |\frac{\partial w}{\partial x_i}|^{p-2}\frac{\partial w}{\partial x_i})}$   .

A Liouville comparison principle for solutions of quasilinear singular parabolic inequalities