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I play a lot of HU and so this comes up a fair bit. I've borrowed from other sources and come up with a simple, very abstract, chase section.

Firstly, it's presumed that the chase is equitable. two people on foot. Good. One car chasing another. good. a man trying to catch a car....not so good (but then again, it'a all in the details). also, it has to be a chase, not a race. two cars on a flat road aren't chasing each other, they are trying to just outspeed each other. it's when two helicopters are pursuing a flying character while he winds through buildings is when you can call it a chase.

1) every round make a check for danger. How often there is danger is a situational thing, but as a rule of thumb, I rule that there is some sort of dangerous obstacle, 10% per round undernormal chase conditions, 20% per round in moderatly crowded conditions and 30% per round in very crowded conditions. If a dangerous obstacle is present, make both parties make a check of some kind (drive automobile, or dodge check) with a penalty depending on severity.

2) Check leads. I tend to make any official chase about how many lengths target and character are far apart. 10 feet on foot, 25 feet in most ground vehicles is a general rule. I then keep track on ho much the pursued has on the pursuer.

3) moves: Obviously each party has a plan for pursuit and evasion, and this is a round by round idea. each party decides on a strategy and states it. then I make both parties make a check and compare them to each other. both strategies get resolved, and more importantly, each startegy changes the lead. (typically, if you defeat your opponent, the lead decreases or increases by one) Exactly what pursuer and pursued want to do is adjucated pretty much on the spot. If bruno is running from the cops, he may wish to evade by Losing them in a crowd (perception check..only good if they are 100 or more feet away) or by zig zagging through winding alleys (d20 add PP, compare to the cops D20+IQ). the cops may want to speed up (D20+Spd vs D20+Spd) or by trying to shortcut ahead of him (IQ Vs IQ).
at any rate, it all ends when the lead gets to 0 or when the lead stertches too far for pursuit (GM's call. If the lead reached 200, then that's 2000 feet. in a crowded inner city, that's probably too far to follow someone effectively)

Obviously it's just a little mechanic to keep things flexible and to make a chase scene seem dramatic.

Batts

The combat part is pretty straight forward, the chase is the fun part. I've found that in order for the characters to not destroy the vehicle they are chasing it has to have something (some one) they want.

I usually do piloting rolls. Since this presumed to be at high speeds other factors such as terrain or even city streets may play into this. Since the characters are so intent on chasing their target are they paying attention to other factors such as other traffic, people and so on. So adjust rolls as you see fit. I think HU may also have penalties and such for high speed combat. On a failed roll for the lead vehicle they could lose speed allowing the chase vehicles to catch up. Likewise if the chase vehicle fails their roll they probably have something in their way, lose speed or or otherwise don't catch up.

This is something that I don't have hard and fast rules for and mostly play it by ear. If I think I can elements to make it more exciting along the way I add them into the chase. Police? School bus full of kids, garbage truck or tractor trailer blocking the intersection, an accident in the way.

Other factors to consider are: Does the party that is running already have a planed escape route? This could give them bonuses in their rolls. Is the party running not know where their going? This could make for a more chaotic chase because they don't know where they'll end up.

I've also found its helpful for the GM to have a general idea of the layout of the chase. Its good to know where all the short cuts, ramps, canyon jumps, bridges, rivers, piers and so on are. Having a map could help too.

Have fun

Carl

Don't forget the road combat rules in TMNT - Road Hogs. 8]

Lot's of pilot/control rolls. The faster the chase, the more uncertainty their is and reliance on the drivers supposed skill.

In my Robotech games, piloting becomes a game of chance once the dogfights and epic explosions begin, but the sweet sound of a player group erupting in cheers and applause makes it all worthwhile!