The wanted and the hunter, we have faced each other many times .... in the past .... Of all those hunted down by her, nobody has ever survived .... except for me
But this time I don't know .... what will happen"
~ Ryoko
The story between Nagi (the bounty hunter) and Ryoko (the space pirate) is obviously one that stems from a deep-rooted past. Nagi, as far as the series explains, has pretty much always been in pursuit of Ryoko. The bounty hunter has tracked the space pirate down in various places in space on a number of occasions and has nearly captured her during a couple of their battles. Though these two have met up with each other many times, Ryoko has always managed to elude Nagi in some form or another. Nagi has been noted for being the absolute best at what she does (according to Galaxy Police Officer, Kiyone) therefore, one can assume that it's probably hard for Nagi to accept any type of failure.
After a period of time in watching the show, the viewer comes to see that Nagi does not really consider her battles with Ryoko to necessarily be failures anymore but .... more of a form of direct competition. In the series, Nagi takes on a rather obsessive attitude toward Ryoko and is constantly trying to prove herself to be the better woman. Nagi's goals are completely unchanging though, she still fully intends to capture Ryoko as a bounty.
Ryoko's intentions toward the bounty hunter have never really been made clear. But, one can assume that she has an imminent respect for Nagi, however this is not to the point of being obsessed. Ryoko seems to go from trying to get rid of Nagi in the series, to kind of just trying to avoid her altogether. When Ryoko first speaks of the infamous bounty hunter, Nagi, she speaks her name in more of a respectful, slightly fearful tone. However, as the series progresses Ryoko's tone toward Nagi goes from one of respect and fear to one of irritation really. Nagi is continually in pursuit of Ryoko and Ryoko is always in the pursuit of happiness and well .... that doesn't include having a bounty hunter on her tail. =^.^=