Using the technique you suggested, I solved the system (of two second-order
 odes de1, de2) for a particular parameter k.
Now suppose I want to do a loop computation for different k values:
sysk := {subs(H[0] = 1, Omega[d] = .274, alpha = -0.1e-2, w = 0, de1), 
subs(H[0] = 1, Omega[d] = .274, alpha = -0.1e-2, w = 0, de2)}
icsys := Delta[d](1) = 10^(-5), (D(Delta[d]))(1) = 0,
             Delta[f](1) = 10^(-5), (D(Delta[f]))(1) = 0

A := []; for e from -1 by .1 to 3 do solk := dsolve({icsys, op(subs(k = 10^e, sysk))}, numeric,

 known = [A, A1, A2, A3]); deltk := subs(solk, Delta[d](t)); 

A := [op(A), [e, log10(deltk(.9)^2)]] end do

and here is the error message I get:
Error, (in dsolve/numeric/process_input) unknown [] specified as
 'known' must be an evaluatable procedure

But A,A1,A2,A3 are defined earlier in the previous 4th order system and
 it had worked for a single k value.

Any idea?

It works, thanks!

That was it!

Thanks for the help, Preben!

That is true. But my question is: how can I save the numerical solutions as a  filename.dat file?

Thanks