  We consider a 2-dimensional thin domain with order of thickness {\epsilon}
which presents oscillations of amplitude also {\epsilon} on both boundaries,
top and bottom, but the period of the oscillations are of different order at
the top and at the bottom. We study the behavior of the Laplace operator with
Neumann boundary condition and obtain its asymptotic homogenized limit as the
parameter {\epsilon} goes to 0. We are interested in understanding how this
different oscillatory behavior at the boundary, influences the limit problem.
