They want brains. You have brains. You may not want to give up your brains. Hence the eternal struggle.
Can be found in the Bradbury basement, or the zombie Mall in gangland. The mall zombies are noticeably tougher than the basement zombies, hitting faster and harder. Mall zombies reward you with slightly more xp then basement zombies but receive the same payout from the zombie contract. They tend to be less camped as well, and seem to swarm less than the basement zombies.
They're a popular grinding target due to the good payout on zombie hunter contracts, and aren't too tough once you can handle crackheads with ease, just remember to pack a mortilex hypo or two, as they can afflict you with zombie rot.
Warning: Zombies have a nasty tendency to swarm, meaning one zombie you're fighting can quickly turn into six zombies you're fighting. This isn't much problem for most people, but newbies moving up from crackheads should be warned of this possibility. If you can kill one zombie with some difficulty (i.e. it takes more than 20 seconds) you should exercise caution when grinding on zombies, lest they dog pile you for your delicious brains. Much like movie zombies, their strength is in their numbers.
A tip for the hyperimmune: you can eat half a zombie meat as soon as you have 1 Hunger and not throw up. The healing adds up!