I'm sure there is a simple answer to this (probably adjusting the nut behind the joystick);  but having read the tutorials to no avail, here I am.  For years I've enjoyed mostly low level VFR flights but recently tried some much longer trips and find the aircraft does not stay on course when left on AP.   

For example, on a recent flight from London to Tokyo I did everything manually for a couple of hours, over eastern Europe I set the course on the AP and went to bed;  the next morning, while the AP and GPS said I was still on course, in reality I was over 300nm north of Tokyo.  Flight analysis showed I had flown in a large arc rather than a straight line.

This is not endemic to one AC or one geographic area, I assume this has always occurred but wasn't particularly noticeable due to the comparatively short flights I normally take.  Since I have neither the time nor the inclination to sit at my computer for more than a couple of hours, how do I keep the aircraft on course during those long flights? 

So much to suggest, jgf.......

First thing is, winds change, as Webb indicates. Beyond that. air pressure changes (meaning that height readings become inaccurate) and compasses deviate (leading to you getting off course). I'm frankly surprised that, using your 'method,' you weren't up to 1,000 nms. off course, instead of just 300.....

As Webb says, the simple way to stay on course is to switch from 'NAV' to "GPS' on the autopilot. That way the course will stay right. But at the expense of the whole flight being as boring as watching paint dry.........

The way to deal with air pressure and compass variations is to press 'B' (for 'barometric') and 'D' (for
'deviation') from time to time. But I'm afraid that that doesn't do much to alleviate the boredom.

My own solution is not to bother with marathon airliner longhaul trips and to make shorter (1,000nm.-2,000nm.) trips in lighter aircraft. And, for good measure, mostly to make 'round-world' trips in them.

Beyond that, I leave 'GPS Hold' alone as much as I can and use 'traditional' VOR-to-VOR navigation as much as possible. VORs usually have a 200-mile range, so it's necessary (and also fun) to plan your trips as far as possible in 'under-400nm. 'legs' as far as you can.

Finally (in my opinion, and I know many will consider it heresy!) to Hell with not using 'accelerated time' on occasion! I tend to concentrate on takeoffs, climbouts, course changes, patches of bad weather, approaches, landings, etc. - and don't hesitate to use say 4X acceleration on the long boring bits.

At least I 'see' the whole flight that way - and don't face the risk of waking up smelling smoke and realising that leaving the 'puter on has set the house on fire......

Beyond that, I find the whole process of planning and carrying out round-world flights in under-2,000nm. legs in smaller (and therefore basically-unsuitable) aeroplanes endlessly satisfying and absorbing; especially using different dates and 'real weather,' and having to cope with all sorts of airfields, including plenty of under-equipped ones.

Don't really have to say much more because, years back, I wrote that approach to FS up in a 'tutorial' which Simviation were kind enough to put on their site. It provides a lot of detail on VOR-to-VOR navigation, route planning, fuel conservation etc. Click on "FS2004 Round The World in A Prop" (sixth one down) if you're interested:-

http://simviation.com/1/browse-Adventures-128-2

PS - about "Flight analysis showed I had flown in a large arc rather than a straight line', you have to blame a guy named Mercator for that. Way back, he devised the "Mercator Projection' - which shows a flat world on a rectangular map. In fact, of course, it's a sphere - so that the 'true route' from A to B follows a curve, not a straight line, on Mercator's map. The navigators' term for that is the 'Great Circle Route.'

With the result that, among other things, on his map, flying the shortest route round the world from Australia to Australia, you'll find yourself flying over Northern Canada....... 

I agree with what Nav had to offer.   I have added autopilot to most everything, except the small aircraft.  Although, having said that, I can remember a time when I didn't use autopilot at all, ever.  Of course, I had lots of problems and spent what seemed like long hours pouring over maps, etc.  Using autopilot and GPS for long flights is all I do anymore.  There are times when I notice that the AC isn't tracking exactly on the path, and there are times when coming in for a landing it is best to simply turn off autopilot altogether.  LOL

I quickly learned the AP is thoroughly inept at landing most of the time, usually bringing me down a few hundred yards short of the runway (no big deal since it's necessary to keep collision detection disabled, but not very realistic).  My procedure now, with larger aircraft, is to let it fly the approach til I have the first doubts, then take over and land manually.  In smaller aircraft I only use the AP for straight and level legs of about 15min or more.

jgf, it's not the AP's job to land you. Its job (when set to the instrument landing system at a given airport) is to line you up with the runway and take you down the glidepath until you're close; then it's up to you to switch it off and finish off the landing manually. Beyond that, it's up to you to make sure that the power is right (not too much, not too little) to maintain landing speed. Too little power and you certainly will 'sink into the ground' - too much and you'll overshoot.

A lot of the fun of FS, to my mind, is working to perfect your procedures and techniques as much as you can so as to avoid those 'doubts' you mention as far as possible.

Here's how you do that:-

http://205.252.250.26/cgi-bin/yabb2/YaBB.pl?board=COF;action=display;num=1111322...

For airports without ILS (except the very smallest ones) the GPS will more or less line you up with your chosen runway (read up under 'GPS' in the Learning Centre for the procedure, it's a bit complicated). However, it will not handle the glideslope for you, and it won't always get the line of the runway exactly right.