  The procedure to find gauge invariant variables for two-parameter nonlinear
perturbations in general relativity is considered. For each order metric
perturbation, we define the variable which is defined by the appropriate
combination with lower order metric perturbations. Under the gauge
transformation, this variable is transformed in the manner similar to the gauge
transformation of the linear order metric perturbation. We confirm this up to
third order. This implies that gauge invariant variables for higher order
metric perturbations can be found by using a procedure similar to that for
linear order metric perturbations. We also derive gauge invariant combinations
for the perturbation of an arbitrary physical variable, other than the
spacetime metric, up to third order.
