Multimodal optical coherence tomography (OCT) is an emerging tool for tissue state characterization. Optical coherence elastography (OCE) is an approach to mapping mechanical properties of tissue based on OCT. One of challenging problems in OCE is elimination of the influence of residual local tissue relaxation that complicates obtaining information on elastic properties of the tissue. Alternatively, parameters of local relaxation itself can be used as an additional informative characteristic for distinguishing the tissue in normal and pathological states over the OCT image area. Here we briefly present an OCT-based approach to evaluation of local relaxation processes in the tissue bulk after sudden unloading of its initial pre-compression. For extracting the local relaxation rate we evaluate temporal dependence of local strains that are mapped using our recently developed hybrid phase resolved/displacement-tracking (HPRDT) approach. This approach allows one to subtract the contribution of global displacements of scatterers in OCT scans and separate the temporal evolution of local strains. Using a sample excised from of a coronary arteria, we demonstrate that the observed relaxation of local strains can be reasonably fitted by an exponential law, which opens the possibility to characterize the tissue by a single relaxation time. The estimated local relaxation times are assumed to be related to local biologically-relevant processes inside the tissue, such as diffusion, leaking/draining of the fluids, local folding/unfolding of the fibers, etc. In general, studies of evolution of such features can provide new metrics for biologically-relevant changes in tissue, e.g., in the problems of treatment monitoring.