I have a 320i,2002,BMW.I have intermittent problems of engine cutting out,at times have to pump accelerator after a cut out to keep engine running 4000-2000 revs .Fuel pump was tested (very good condition),fuel filter was replaced,plugs,air filter and oil.It seems when the cutting out occurs,the yellow oil light appears to indicate low oil level,but level is full.Can someone give a solution to this problem please.

USA CAR,NOT tOLD yours.nor "e"code, series3 code.
e21 ,1975?
2.0L
320i. the "i' only means fuel injected 320d is diesel
what matters more 'e" code, e21 up.
No year told,
NO ENGINE told, nOR GAS OR DIESEL.?????? i= gas.
first we test fuel last , not pumps first (sorry but i cover that)

the engine must be good, no bad engine burns fuel and run.
next is (gas engine) spark must be good or if diesel glow plugs.working.
then comes fuel checks last. (all this is basic basics 101 stuff)
the PCm cuts fuel for many good reasons.
but we test fuel pressure cranking, on any dead engine using a tool called fuel gauge ( PSI or in Europe BAR/kPA)
CRANKING ONLY
IF THE FUEL PUMP RELAY IS DEAD, MOST TIMES THAT MEANS
THE PCM IS CUTTING FUEL ON PURPOSE.
TOP CASE PCM SEES SPARK DEAD AND MUST BY LAW CUT FUEL FAST.
if car has bad TPS sensor and it sends 5vdc to the PCM for throttle angle (100^%) or WOT false signal the PCM cuts fuel
or the PCM sees IMMO not happy it cuts fuel. or spark and on some cars even cuts cranking, on my car it cuts fuel after 3 second run
if IMMO KEY FAILS.

other simple tests, is Test fuel.spray
if engine good and spark good, test fuel works.
see? but no engine told
and spark plugs all tested for good spark..
on on all uSA cars here, 1996 up any OBD2 scantool works
so we scan it first. see why the PCM cut fuel???
as it can for many reasons,
on gasoline engine top causes are P03xx DTC errors
for sure CMP or CKP sensors failing it cuts fuel 1or2 ways.

NO CAR TOLD at all.
47 year span , sorry can not guess.

The year the first BMW 320i was manufactured was 1975
Max Nebular car.

fuel is cut to prevent CRASH and burn as seen on TV, endless.
by law and pure hard LOGIC. deep inside the PCM.
and more.

Re-Check your spark plugs again take each one out & make sure the gap is set at 24 on every plug, if this is not electric problem then look at the fuel your fuel pump cleaner may be blocked up both jobs are DIY as long as your technically minded. Cheers, Malcolm Campbell.

More detail needed. Is the clutch dragging causing the engine to stall?
Does it otherwise idle OK?
Any fault codes?

General advice:
Radio interference.
Ceck alternator recharge rate.
Very low on details,u mean if in a parking lot it will iddle fine?If breaking hard won't stall?If easy break engage won't cut?
Fuel/Fuel line/fuel pump related issues.
Air mass (MAF) sensor related.
U must track the problem,more details.
Cheers,share if figured out.

the big air intake pipe going to the throttle boddie usually split causing low revs poor acceleration and cutting out i would chect this first

if this helps let me know

cheers
mike

What about the fuel pump?

The 4 main reasons usually why a vehicle just cuts off are as follows 1 restricted fuel flow which you could rule out easily if the vehicle sputters or hesitates lets say climbing a hill or under heavy acceleration 2 a faulty map (manifold absolute pressure) low barometric pressure signal received can cause vehicle to cut out 3 a faulty idle control circuit which is usually preceded by an erratic idle but not always 4 a faulty maf (mass air flow sensor) which over time the probe can build up residue and cause vehicle to idle or rev up erratically or cause your vehicle to cut out as well. I'd have it checked for trouble codes whether the engine light is on or off and you can have a full diagnostic scan which would systematically check the vehicles sensors and functions before replacing any unnecessary parts

Whens the last time it was tuned up? plugs, wires, cap and rotor,(if you have them), Air filter and fuel fliter. Any one and all of these can cause your problem.

i had the same problem and it was infact the timing and chain tensioners

sounds like the fuel pump in youre fuel tank at fault try hitting the tank whilst someone cranks the engine ensure its in neutral and cant roll away if it then starts you will need a new pump