The singularly perturbed equation with delay of the form \[ \varepsilon \frac{dx}{dt}+x(t-\varepsilon h)=F(x(t-1)) \] is considered. Here, with \(h>0\), \(0<\varepsilon\ll 1\), \(F\) is a quasilinear function with \(F(x)=ax+\mu f(x)\), \(0<\mu\ll 1\), \(f\) is a continuous function with \(f(0)=0\). Dynamic properties of solutions to this equation are studied. It is shown that the parabolic Ginzburg-Landau equation may be regarded as the normal form of the equation under study when \(F(x)=ax+bx^2+cx^3+O(x^4)\).