The single-particle spectral functions A(k,omega) and self-energies Si
gma(k,omega) are calculated within the t-J model using the finite-temp
erature Lanczos method for small systems. A remarkable asymmetry betwe
en the electron and hole part is found. The hole (photoemission) spect
ra are overdamped, with Im Sigma proportional to omega in a wide energ
y range, consistent with the marginal Fermi liquid scenario, and in go
od agreement with experiments on cuprates. In contrast, the quasiparti
cles in the electron part of the spectrum show weak damping.