This is very good question. In fact during the stance all extensors of the lower extremity muscle group are involved; such as the gluteus, (hip extensors) the vastus medialis and lataralis, (kne extensors) and the soleus with gastrocnemius (ankle extensor). for the swing phase it is mostly at the initial swing are the flexors the momentum takes over.      

Actually, the stance phase in race walking is not "stance" like in normal walking. It's a propulsive phase, so as soon as the foot contacts the ground the gluteus and the biarticular flexors are mainly involved. The calves work mostly in the final phase.

The swing phase involves not only, as in normal walking, the biarticular extensor muscle, namely the rectus femoris,  but all the quadriceps muscles, since it is needed an extremely strong extension, even hyperextension. 

Dear Marco,

In away you are right but the knee flexor stabilize the joint during the stance phase. Again during the swing phase hip flexors initiate the swing and the gluteus control it. Any way EMG studies showed this timing.

Thank you very much. I wonder if walking at gradually increased speed may affect significantly the activity of the muscles. I mean is a changing speed a strong stimulus for the action potentials of the muscle?

Dear Wanda

You may try http://onlinelibrary.wiley.com/doi/10.1002/jor.1100020309/abstract;jsessionid=6FDE5A3DC3F826FE1A15BB10614DE6A2.f01t01

and this

http://www.sciencedirect.com/science/article/pii/0013469485911083

These 2 articles are old but essential

Dear Hashem,

since the question was on RACE walking (12, 13, 14 km/h and more, as for people I followed for many years), that is very different from fast walking (6, 7, 8 km/h) the biomechanic is very different, and it's important to not confuse them.

warm regards

Thank you. So Marco, may I ask you for some information. I would be appreciated.

Best regards