Scanning electrochemical microscopy (SECM) has been employed in the feedback mode to assess the electrochemical behavior of two-dimensional networks of single-walled carbon nanotubes (SWNTs). It is shown that, even though the network comprises both metallic and semiconducting SWNTs, at high density (well above the percolation threshold for metallic SWNTs) and with approximately millimolar concentrations of redox species the network behaves as a thin metallic film, irrespective of the formal potential of the redox couple. This result is particularly striking since the fractional surface coverage of SWNTs is only approximately 1% and SECM delivers high mass transport rates to the network. Finite element simulations demonstrate that under these conditions diffusional overlap between neighboring SWNTs is significant so that planar diffusion prevails in the gap between the SECM tip and the underlying SWNT substrate. The SECM feedback response diminishes at higher concentrations of the redox species. However, wet gate measurements show that at the solution potentials of interest the conductivity is sufficiently high that lateral conductivity is not expected to be limiting. This suggests that reaction kinetics may be a limiting factor, especially since the low surface coverage of the SWNT network results in large fluxes to the SWNTs, which are characterized by a low density of electronic states. For electroanalytical purposes, significantly, two-dimensional SWNT networks can be considered as metallic films for typical millimolar concentrations employed in amperometry and voltammetry. Moreover, SWNT networks can be inexpensively and easily formed over large scales, opening up the possibility of further electroanalytical applications.