In his ergodic theoretical proof of the celebrated Szemeredi theorem, H. Furstenberg introduced "nonconventional ergodic averages" which are averages of quantities f.Tⁿ f.T²ⁿ f.T³ⁿ … f.T^kn (f an L^∞ function, k a fixed integer, T a measure preserving transformation). It was sufficient, to obtain the combinatorial application, to prove, in case f=1_A, that the lim inf of these averages was >0. The issue of the L² convergence remained open until 2005 when it was solved by Host and Kra using deep structure theorems. The extension to the nonconventional averages f₁.T₁ⁿ f_2.Tⁿ …f_kT_kⁿ, (f_i L^∞ functions, T_i k commuting measure preserving transformations) remained open until a proof of the L² convergence was given by T. Tao in 2007. Since, another proof was produced by T. Austin, using a completely different approach. B. Host, afterwards gave another proof with some connections to Austin's. We are going to present an alternate proof, irrelated to the previous ones, essentially based on the tool of joinings.