The single-particle spectral functions A(k, ω) and self-energies Σ(k, ω) are calculated within the t−J model using the finite-temperature Lanczos method for small systems. A remarkable asymmetry between the electron and hole part is found. The hole (photoemission) spectra are overdamped, with ImΣ ∝ ω in a wide energy range, consistent with the marginal Fermi liquid scenario, and in good agreement with experiments on cuprates. In contrast, the quasiparticles in the electron part of the spectrum show weak damping.PACS numbers: 71.27.+a, 79.60.-i, 71.20.-b The normal state of superconducting cuprates in many aspects contradicts the phenomenology of the normal Fermi liquid (FL). Anomalous frequency and temperature dependence of several response functions is generally attributed to electronic correlations, yet a proper description is missing so far. The angle resolved photoemission (ARPES) experiments [1-3] probe the one-particle spectral function A(k, ω). At intermediate doping they reveal for a wide class of cuprates a well defined large Fermi surface (FS) consistent with the Luttinger theorem and similar quasiparticle (QP) dispersion [2]. This seems to imply the validity of the concept of the usual metal with electronic-like FS. Such simple FL picture is in an apparent contradiction with magnetic and transport properties, e.g. electrical conductivity scales with hole concentration, closer to the picture of holes moving in the antiferromagnetic (AFM) background. Moreover, in ARPES the FL interpretation is spoiled by the overdamped character of QP peaks [3,2]. Although a large background makes fits of particular lineshapes non-unique [3,4], the QP inverse lifetime is found to be of the order of the QP energy, i.e. τ −1 ∝ ω for ω > T , leading to the concept of the marginal Fermi liquid (MFL) [5] with an anomalous single-particle and transport relaxation, in contrast to τ −1 ∝ ω 2 in the normal FL.It is unclear whether above features can be reproduced within generic models of strongly correlated systems, such as the Hubbard and the t − J model, in particular in the most challenging regime of intermediate doping. Spectral properties of these 2D models have been so far studied mainly via numerical techniques [6], e.g. exact diagonalization (ED) [7] and Quantum Monte Carlo (QMC) [8]. These studies, as well as some analytical approaches [9], established a reasonable consistency of the model QP dispersion with the experimental one, as well as the possibility of large FS, but have not been able to investigate closer the character of QP, being in the core of the anomalous low-energy properties.The aim of the present work is to employ the finitetemperature Lanczos method [10] to calculate A(k, ω) within the t − J model. This method has been already applied to other dynamic [11] and static [12] functions, yielding features consistent with the MFL concept and experiments on cuprates. Although calculations are still done in small systems, by using finite (but small) T > 0 smooth enough spectra are obtained not only to determ...