a=1;
c=1;
tw[x0_]:=Log[Log[a]-Log[x0]]/c;
x[t_,x0_]:=a E^(-E^(c(tw[x0]-t)));
bild1=Plot[x[t,0.2],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild2=Plot[x[t,0.4],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild3=Plot[x[t,0.6],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild4=Plot[x[t,0.8],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild5=Plot[x[t,0.1],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild6=Plot[x[t,0.01],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild7=Plot[x[t,0.001],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild8=Plot[x[t,0.0001],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild9=Plot[x[t,0.00001],{t,0,10},PlotRange->All,DisplayFunction->Identity];
bild=Show[{bild1,bild2,bild3,bild4,bild5,bild6,bild7,bild8,bild9},
PlotRange->{{0,10},{0,1.1}},AxesLabel->{"t","x"},
ImageSize->{400,300},DisplayFunction->$DisplayFunction];