In the field of tissue engineering, in order to restore tissue functionality hydrogels that closely mimic biological and mechanical properties of the extracellular matrix are intensely developed. Mechanical properties including relaxation of the surrounding microenvironment regulate essential cellular processes. However, the mechanical properties of engineered hydrogels are particularly complex since they involve not only a nonlinear elastic behavior but also time-dependent responses. An accurate determination of these properties at microscale, i.e. as probed by cells, becomes an essential step to further design hydrogel-based biomaterials able to induce specific cellular responses. Atomic Force Microscopy (AFM) with contact sizes of the order of few micrometers constitutes an appropriate technique to determine the origin of relaxation mechanisms occurring in hydrogels. In the present study, AFM force relaxation experiments are conducted on chemically and physically crosslinked hydrogels respectively based on a synthetic polymer, polyacrylamide and a natural polymer, a bacterial exopolysaccharide infernan, produced by the deep-sea hydrothermal vent bacterium, Alteromonas infernus. Two distinct relaxation mechanisms are clearly evidenced depending on the nature of hydrogel network crosslinks. Chemically crosslinked hydrogel exhibits poroelastic relaxations, whereas physically crosslinked hydrogel shows time-dependent responses arising from viscoelastic effects. In addition, two relaxation processes are revealed in ionic physical hydrogel originating from chain rearrangement and breaking/reforming of the ionic crosslinks. The effect of the ionic strength on both the long-term elastic modulus and relaxation times of physical hydrogels was also shown. These findings highlight that physical hydrogels with well-defined time-dependent mechanical properties could be tuned for an optimized response of cells.