We investigate the dynamical spin-spin and charge-charge correlation f
unctions, S(Q,w) and N(and,w), for the two-dimensional t-J model, by u
sing the exact diagonalization technique. At high electron density (fo
r example, 12 electrons in a 4x4 unit cell), S(Q,w) shows pronounced p
eak at low energy of order J and is consistent with 2k(F) low energy e
xcitations, whereas N(Q,w) consists of a dense and broad continuum, wh
ich is absent from the one-dimensional system. The statistics of eleme
ntary charge excitations is also discussed.