Rotary mechanisms are commonly used for transferring rotational movement in diverse industrial applications in mechanical engineering. Components such as gears and rolling bearings have found their purpose in various automotive, machinery or agriculture systems. During operation in mechanisms, they are subjected to defects or changes of their key parameters. This paper considers the application of recurrence plots (RP) and recurrence quantification analysis (RQA) in the detection of teeth crack in a planetary gear system and radial internal clearance (RIC) in a double row self-aligning ball bearing. Raw signals are obtained from accelerometers installed in test rigs. The analysis consists of a statistical analysis approach and calculations of basic RQA parameters i.e. recurrence rate, determinism and length of the longest diagonal. In the paper, we extract information about the fault detection in one of the rotary systems and about bearing operational parameters with nonlinear dynamics identification.