Given p≧1, letXbe a real-valued, continuousN-parameter process, submitted to a “domination condition” which ensures the existence of itskth variations μX(k) 1≦k≦k0p-stochastic measures which are the multi-parameter analogues of the “variation”dXand the “quadratic variation” d[X] of one-parameter semimartingales. This condition is fulfilled for example for processes of integrable variation, for the (N,1)-Wiener process W,or, more generally in case N=2, for those “representable semimartingales” (Wong Zakai or Guyon, Prum) which have sufficiently well-behaved representing functionals. Furthermore, it allows us to establish a stochastic calculus in Lpsense forXwith a simple version of Itô's formula in terms of the integrals ofμX(k),1≦k≦k0.