Two-dimensional magnetic fluid foams are cellular structures whose fra
mework is made of magnetic fluid. The features of these equilibrated p
atterns are driven by a control parameter: the amplitude of the applie
d magnetic field. When the latter is rapidly increased, an instability
occurs: the walls between cells undulate. Such an instability has als
o been observed in other 2D cellular structures, which exist for insta
nce in Langmuir monolayers or in magnetic garnets thin films. In this
paper we give a theoretical analysis of this instability, the issues o
f which are shown to be well confirmed by experiments and numerical si
mulations.