Chapter 9 of Maseches Nazir, Mishnah 1. The Mishnah comes to establish upon whom the laws of nezirus take effect and upon whom they do not, and in the course of this it compares the nezirus of a woman with the nezirus of a slave.
"HaGoyim ein lahen nezirus":
A non-Jew has no concept of nezirus. Even though a non-Jew may bring certain offerings - vows and voluntary gifts, gift offerings and optional offerings - if he accepts a vow of nezirus upon himself he has no status of a nazir: he is permitted to drink wine and he is not prohibited from tumah. And even as a matter of law itself, by Torah law a non-Jew does not become tamei at all.
"Nashim va'avadim yesh lahen nezirus":
Women and slaves are Jews, and even a Canaanite slave is counted for this purpose as part of Israel, and therefore the laws of nezirus apply to them.
From here the Mishnah continues and sets two stringencies one against the other:
"Chomer banashim mibe'avadim - shehu kofeh es avdo v'eino kofeh es ishto": A master has the power to force his slave to violate his nezirus, and this control is given to him. A husband, by contrast, cannot force his wife to violate her nezirus. If he wishes to cancel it, he has the power to annul it, and just as he annuls her vows in general so too he annuls her nezirus; but he has no power to leave the nezirus in force and compel her to violate it.
"Chomer ba'avadim mibanashim - shehu meifer nidrei ishto v'eino meifer nidrei avdo": A husband can stop his wife's vow and the vow is void, whereas a master has no power at all to annul his slave's vows.
A further difference - the force of the annulment:
"Hefer l'ishto - hefer olamis": The annulment is permanent, and even after they are divorced the vow does not return and take effect again.
"Hefer l'avdo": Here there is no annulment at all, since a master has no power to annul for his slave, but only to compel him to violate his nezirus for the time being. Therefore "yatza l'cheirus - mashlim nezirusso": from the moment he goes free, the nezirus stands in force and he is obligated to complete it.
A slave who ran away from his master:
"Avar mikeneged panav" - a slave who accepted nezirus upon himself and fled from his master. In this case the Tannaim disagreed: "Rabbi Meir omer: lo yishteh" - during the time of his flight he must keep his nezirus and he does not drink wine. "Rabbi Yosi omer: yishteh" - he does not observe the nezirus while he is a fugitive.
The reasons for the dispute in the Gemara:
Rabbi Meir's approach: The case is one in which his master does not want him to keep the nezirus, and nevertheless he must keep it - because we penalize the slave by requiring him to keep his nezirus. Nezirus is generally a hardship, and as a result he will return to his master, and once he is under his master's control his master will be able to cancel the nezirus for him and he will be permitted to drink wine.
Rabbi Yosi's approach: He is permitted to drink wine even when he is not before his master, since ultimately he is still in his master's domain, and the master does not want him to observe nezirus - so that he should not become weak and unable to work properly.
In summary: In this Mishnah we learned that non-Jews have no nezirus, whereas women and slaves do have nezirus. We saw the stringency regarding women - that a master forces his slave to violate his nezirus while a husband does not force his wife, and the stringency regarding slaves - that a husband annuls his wife's vows while a master does not annul his slave's vows. We also learned that a husband's annulment for his wife is a permanent annulment, whereas a slave who goes free completes his nezirus, since it was never annulled. And finally, Rabbi Meir and Rabbi Yosi disagreed about a slave who ran away from his master: according to Rabbi Meir we penalize him by requiring him to observe the nezirus so that he will return to his master, and according to Rabbi Yosi he is permitted to drink wine, since his master does not want him to become too weak to work.