Convergence of derivative expansions in scalar field theory

The convergence of the derivative expansion of the exact renormalisation gr oup is investigated via the computation of the P function of massless scala r lambda phi (4) theory. The derivative expansion of the Polchinski flow eq uation converges at one loop for certain fast falling smooth cutoffs. Conve rgence of the derivative expansion of the Legendre Row equation is trivial at one loop, but also can occur at two loops and in particular converges fo r an exponential cutoff.