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Run a bottle of Techron injector cleaner through the gas and see if your
failure to start problem goes away. Read what your manual says about
'starting a flooded engine'. Next time it won't start hold the gas pedal
like the manual suggests and see if it starts with a puff of black
smoke. Confirmed.

'Curly'

I checked the coolant and it is okay.  The battery is a Honda battery
replaced by the Honda dealer in December, 2006, so I doubt that could
be a problem.  I've done a little research and the things that come up
are: throttle body & the EGR thing and the main relay.  As I said
before the main relay was replaced last year.  Could a dirty throttle
body cause both the hesitation and the starting problem?  Why would
both things happen at once?

Thanks,  Bridget.

I would start by checking the coolant in the cooling system
reservoir. If it's not between the max and min lines, then
fill to the max line.

Certain engine control sensors must be immersed in coolant
to work properly. If the coolant is at all low, they may not
be immersed. The sensors then send the wrong signal to the
fuel and air control systems.

Especially if the coolant was recently replaced, do this. It
costs little and is a common cause of the problem you
describe.

There are others. Start here, though.

Please confirm whether
-- OEM ignition wires and spark plugs were used
-- the air and fuel filters were replaced. If not, when were
they last replaced?
-- the battery is old. This is for the slow-to-catch
problem. Battery age in years and miles, please? What make
of battery is now installed? Do you have a multimeter to
check its voltage with the car off and on?

I have a 93 Accord EX with 158K miles, 5 speed manual, with an
intermittent problem.  It sometimes hesitates while accelerating at
low rpm. It happens when I shift to 2nd or from 2nd to 3rd or when
going around a corner in 3rd and then trying to accelerate.  It seems
to go away when the rpms get higher.

The main relay was replaced in June 06 when the car would not start
(crank but not start).  This hesitation/jerking/stumbling problem is
recent.  Last week I had a tune-up at Honda dealer - spark plugs were
replaced and timing, belts, hoses & filters were checked.  The fuel
relay (Relay RZ 39400-SM4) was replaced.  It did not fix the problem.

Also, sometimes when I start the car it sounds like it isn't going to
catch but then does.  Again, it doesn't do this all the time.

Any ideas on how to fix this problem without replacing everything in
the car?

Thank you for any advice.