For nonlinear hyperbolic problems, conservation of the numerical scheme is importantfor convergence to the correct weak solutions. In this paper the conservation of the well-known compact scheme up to fourth order of accuracy on a single and uniform grid isstudied, and a conservative interface treatment is derived for compact schemes on patchedgrids. For a pure initial value problem, the compact scheme is shown to be equivalent toa scheme in the usual conservative form. For the case of a mixed initial boundary valueproblem, the compact scheme is conservative only if the rounding errors are small enough.For a patched grid interface, a conservative interface condition useful for mesh refinementand for parallel computation is derived and its order of local accuracy is analyzed.