The oscillatory behavior of the neutral parabolic differential equation with continuous deviating arguments of the form \[ D_t \left[ u - \sum^m_{i = 1} c_i (t) u(x,t - r_i) \right] = a(t) \Delta u - p(x,t) u - \int^b_a q(x,t, \xi) f \biggl[ u \bigl( x,g (t, \xi) \bigr) \biggr] d \sigma (\xi) \] for \((x,t) \in \Omega \times R_+\), are reduced to the existence eventually no positive solutions to some ordinary differential inequalities.