Among different approaches to the search for novel—safer and less addictive—opioid analgesics, biased agonism has received the most attention in recent years. Some μ-opioid receptor agonists with G protein bias, including SR compounds, were proposed to induce diminished side effects. However, in many aspects, behavioral effects of those compounds, as well as the mechanisms underlying differences in their action, remain unexplored. Here, we aimed to evaluate the effects of SR-14968 and SR-17018, highly G protein-biased opioid agonists, on antinociception, motor activity and addiction-like behaviors in C57BL/6J mice. The obtained results showed that the compounds induce strong and dose-dependent antinociception. SR-14968 causes high, and SR-17018 much lower, locomotor activity. Both agonists develop reward-associated behavior and physical dependence. The compounds also cause antinociceptive tolerance, however, developing more slowly when compared to morphine. Interestingly, SR compounds, in particular SR-17018, slow down the development of antinociceptive tolerance to morphine and inhibit some symptoms of morphine withdrawal. Therefore, our results indicate that SR agonists possess rewarding and addictive properties, but can positively modulate some symptoms of morphine dependence. Next, we have compared behavioral effects of SR-compounds and PZM21 and searched for a relationship to the substantial differences in molecular interactions that these compounds form with the µ-opioid receptor.