Great! It works! Thank You Very Much, Shausend!

Here's a piece of code providing the result which i have been trying to obtain for the last three days /ODE system was amplified with one more equation, but it doesn't influence on behavior of u[t] at all/:

Code:

k1=25;k2=0.3;k3=0.04;k4=0;k5=0.27;
k6=0.98;k7=0.002;k8=0.03;k9=0.004;k10=100;nt=10
result := NDSolve[{u'[t] == (k6 - u[
t])*k1 + (v[t] - u[
t])*k2, v'[t] == (u[t] - v[t])*k3, w'[t] == (k8 - w[t])*k1 + (u[t]*(
1 - v[t]) + v[t]*(1 - u[t]) - w[t])*k4 + (2*v[t](1 - v[t]) - w[t])*k5,
u[0] == k7, v[0] == k7, w[0] == k9}, {u[t], v[t], w[t]}, {t, 0, k10}]
uf[t_] = First[Evaluate[u[t] /. result]]
wf[t_] = First[Evaluate[w[t] /. result]]
pfr = Table[
result := NDSolve[{u'[t] == (uf[t] - u[t])*k1 + (v[t] - u[t])*k2, v'[
t] == (u[t] - v[t])*k3, w'[t] == (wf[t] - w[t])*k1 + (u[t]*(1 - v[
t]) + v[t]*(1 - u[t]) - w[t])*k4 + (2*v[t](1 -
v[t]) - w[t])*k5, u[0] == k7, v[0] == k7, w[0] == k9}, {u[t], v[t], w[
t]}, {t, 0,
k10}]; uf[t_] = First[Evaluate[
u[t] /. result]]; wf[t_] = First[Evaluate[w[t] /. result]];
{uf[t], wf[t]}, {n, 2, nt}]
Plot[{0, uf[t], wf[t], 1}, {t, 0, k10}]
output := Table[tr := n; {t, uf[tr], wf[tr]}, {n, 1, k10}]
Export["output.dat", output]

See the picture plotting in Mathematica. These curves are exactly the things I wanted to obtain.

By the way, i tried to apply this algorithm to the "For" procedure, but it didn't work. I didn't know that Table is more convenient for such purposes in Mathematica.

Not sure why those 6 and more are flat lining though

Because the range of arguments in plots is strangely small.

One small problem is still leaving: in "out" log there are too much lines with "Interpolating function..." appearing as a result of '=' operation inside the table. it is not good if number of steps nt is 500, all this inscriptions are unnecessary for me. How to disable this option in "Out"? I want to see only the plot graph.