Defective speed sensor on one of the wheels.

ABS sensor probably.. I wrote this for a forum I go to.. can help you do the
job yourself.. I've also done the rear ones too.. you'll need a drill to
drill out the old sensor..

***** POST *****
Firstly, I didn't think all this up myself I used some other posts on the
site... one from cotty in particular..

http://www.e36coupe.co.uk/forum/viewtopic.php?t=24908&highlight=abs+resistence+r
esistance

Which can be found there, but I thought I'd write up what I did when my ABS
light came on, because I haven't found a complete guide to the repair as of
yet on here..

First job is to test the sensors, from what I have read the front sensors
tend to go more frequently, so I'd start with those. They are also easier to
test.  You'll need a voltmeter, very sensitive (milli-volts), you can
measure the resistance too, but I found that difficult (see cottys post).
Anyway.. remove the front wheel you're looking at, the sensor is located
within the wheel hub, but the connector in question is actually located
behind a black plastic casing, which is attached to the inside of the wheel
arch.  One of the front wheels will also have a break pad sensor.  Basically
trace the cabling from the hub to the plastic cover attached to the back of
the wheel arch and open it.. The ABS sensor connector should be grey.  The
black connector is for the brake pad wear sensor, and we won't need to look
at that.

Disconnect the grey connector, the top comes off leaving one half connected
to the car electronics (wire leading into engine bay) and the other attached
to the sensor... from Cotty's post we're interested in pins 2 and 3 only.
Use a small bit of wire and hold them onto pins a and 2 and connect your
meter to these.  This is fiddly, and be careful not to bend the pins! (I did
this on one sensor.. and fortunately for me it turned out to be the one that
was duff!) once connected set the voltmeter to milli-volts AC and rotate the
hub, the voltage should rise and lower with the hub speed.  If is doesn't,
my advice is persist a while to see if you have made a mistake with the
settings on the meter, or the wires are not in contact with the pins, a
little time and effort is a good thing, you'll only have to repeat it later
if you're not sure you got the right readings which means more time wasted.
Repeat this step for both the front wheels, if you find a duff sensor, my
advice is continue to check the others, sometimes more than one fails.

The rear sensors are a little different, again one wheel will have the brake
pad sensor, I found mine to be the opposite side to the front.  To do the
rear sensors, I found jacking the car at the back leaving the wheels on.. to
be sufficient (please be carefull when jacking the back don't want people
with cars dropped on their heads! good idea to use stands and blocks for the
front wheels to be secure).  I didn't remove either of the rear wheels.  The
sensor connectors once again are found in a black pastic like case that you
can open, one for each side, although for this they are tucked a little
further back.  Best idea is trace the cables back from the sensors in the
hub to find them.  Again same procedure, open the plastic covers, and take
out the grey connector, and separate it.  There are only 2 pins in these
sensors, so it makes it easier, connect your voltmeter, same settings to
this and (making sure your handbrake is off) rotate the wheels.  This is
where the jacking of the whole car comes in handy.. I found it hard rotating
the hub with the wheels off, with them on you can get more torque on the
wheel.  Again the voltage reading should increase with the speed of the hub
rotation.  And again, make sure that you have accurate readings and your
wires are secure.. will save time later.. don't want to do this again, it's
messy and unpleasant under the back!

By now hopefully one of these sensors will have shown NOT to change voltage
when the wheel spins.  This is our target, buy a new sensor to replace it
from German Swedish French car parts, about 60 quid ish..  In my case it was
front right (51+vat), so I can talk you through the changing procedure for
the front sensors (which is a 5h1t to get out).  Rear I am sure will be
similar.

Remove the wheel again, jack nice and securely, I also turn the wheels
left.. (for right side) so I can get a better view of the sensor.  Remove
the allen key bolt that holds the sensor in place.  You'll notice on the hub
there is a small cab which can be removed with an allen key.  This is a cap
for the sensor, it lines up directly with it from the front and allows you
to insert a rod to use to push the sensor out this way.  The sensors fit
using what I think is called and "interference fit" which means they are
VERY tight to get both in and out... Drilling out the sensor can loosen it
but I would try others ideas (I don't know who suggested it but it was not
me.. don't want to steal anyone elses thunder) soaking it in WD40 (do NOT
get it on your discs!) over night can be a good idea they get pretty stuck
in there.  Be prepared for a long slog they are horrible to get out.
Inserting the sensor is not as hard but is not easy, again the purpose of
the interference fit is to jam the sensor in firmly.. which is really what
we want from this!  once the new sensor is fitted, make sure you replace the
cap you removed from the hub, re connect the sensor, making sure the wires
are clipped where the previous wires were clipped.  I gave my arches a good
clean up too while I was in there.  Re-fit the wheel and drop the car back
down... Go to start, and in theory the ABS light should flicker and go off.
In my case the car did not even need to be started or moving....

I hope this helps anyone with ABS problems in future.. If anyone wants to
add anything to it or correct anything please do so...

Cheers all...

*** POST END****

Hope it helps...