We study multivariate secant methods for the solution off systems of nonlinear equations in complex n-dimensional space $(1 \leqq n < \infty )$. We prove a quantitative theorem about the convergence of such methods and consider the dependence of the order of convergence on the position of the iteration points by using the concept of a set of admissible approximations. We also find the maximal order of the so-called “standard information” $\mathcal{N} = \{ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {f} (\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {x} _j ):j = n,n - 1, \cdots ,0\} $ with respect to the sets of admissible approximations.