Hi Avidaan,

There are some ; missing in the For loop. Better to use Table. Is this what you are looking for?

Module[{a = 0 , t0 = 0, tf = 10^(-9), dt = 2*10^(-10), m1val = {0, 1, 0}, m2val = {0, 0, 1}},
 Table[
  If[
   EvenQ[a], 
   sol1 = 
    NDSolve[{m1'[t] == LL1[Subscript[H, sp][m1[t]]], m1[j] == m1val}, 
     m1, {t, j, j + dt}, MaxSteps -> \[Infinity]];
   Evaluate[m1[t] /. sol1][[1]];
   m1val = Evaluate[m1[t] /. sol1][[1]] /. {t -> j + dt};
   a++;
   {sol1, m1val}, 

   sol2 = 
    NDSolve[{m2'[t] == LL2[Subscript[H, sp][m2[t]]], m2[j] == m2val}, 
     m2, {t, j, j + dt}, MaxSteps -> \[Infinity]];
   Evaluate[m2[t] /. sol2][[1]];
   m2val = Evaluate[m2[t] /. sol2][[1]] /. {t -> j + dt};
   a++;
   {sol2, m2val}
   ],
  {j, t0, tf, dt}   
  ]
 ]