Nagel makes clear that "[b]y altruism I mean not abject self-sacrifice but merely a willingness to act in consideration of the interests of other persons, without the need of ulterior motives." The primary problem to which he devotes his attention is not what sorts of behavior we are thus committed to, but the more fundamental one of how it is possible for such considerations to motivate us _at all_.
I shall not try to summarize his arguments here; this work was published long enough ago that critical evaluations of them are available elsewhere (e.g. in Christine Korsgaard's _The Kingdom of Ends_). Suffice it to say that they involve Nagel's usual tension between the personal and impersonal points of view -- that is, between subjectivity and objectivity -- and the attempt to find some resolution or balance between them (a theme which runs through much of his work and indeed which he seems to have staked out as his own philosophical territory).
At any rate his conclusion is that it is entirely rational for us to be thus motivated and that "rational altruism" is a genuine possibility.
And perhaps most importantly of all, Nagel has stated the _problem_ correctly. I realize this may not be a big deal to some of Nagel's readers. But personally I find it a blessed relief, as I spend a good deal of time reading and criticizing the works of Ayn Rand and her followers; it is a pleasure to read an argument about altruism that gets the issue straight and recognizes that other-regard is simply not reducible to prudence.
Which it isn't, and Nagel's mostly lucid work on this topic has the merit of making this point utterly clear. Readers of David Kelley's _Unrugged Individualism_ and Tibor Machan's _Generosity_ should probably attempt, at some point, to come to terms with the arguments in this volume.