As in conventional 1H MRI, T1 and T2 relaxation times of hyperpolarized (HP) 13C nuclei can provide important biomedical information. Two new approaches were developed for simultaneous T1 and T2 mapping of HP 13C probes based on balanced steady state free precession (bSSFP) acquisitions: a method based on sequential T1 and T2 mapping modules, and a model-based joint T1/T2 approach analogous to MR fingerprinting. These new methods were tested in simulations, HP 13C phantoms, and in vivo in normal Sprague-Dawley rats. Non-localized T1 values, low flip angle EPI T1 maps, bSSFP T2 maps, and Bloch-Siegert B1 maps were also acquired for comparison. T1 and T2 maps acquired using both approaches were in good agreement with both literature values and data from comparative acquisitions. Multiple HP 13C compounds were successfully mapped, with their relaxation time parameters measured within heart, liver, kidneys, and vasculature in one acquisition for the first time.