Non-subscribers please note!
Eric's material on the Tromp here at Chess Publishing is particularly good; hardly surprising in that he's played it many times as White and annotated over a dozen of his own games for us.

Concerning 2...d5 he wrote

"This is without a doubt the most solid response to the Tromp. Black grabs a fair share of the center and challenges White to break down his firm defensive foundations. The main problem with this line for Black, is that it offers few real winning chances."

In my own games against a 2200 Tromp specialist at my club I've found it difficult after 3 Bxf6 exf6 to play against White's plan of setting up a solid dark-square pawn structure (including g3, Bg2) and then gradually preparing the c4 break.

I notice that recent black repertoire books endorse 2...e6, which grabs the bishop pair without any deterioration of the pawn structure after 3 e4 h6, but there are three possible problems:
1) as Lev Alburt argues, below a certain level the "advantage" of the two bishops is worthless and knights are more useful.
2) White gets the centre and a game that is much easier to play, especially at a fast time limit. Black's much-vaunted flexible pawn structure can in fact be a headache to organize.
3) White is not even compelled to play 3 e4; some specialists such as Miladinovic play 3 e3 with success.

For 2...Ne4, Kotronias seems to be the man to watch, but the lines are very concrete and who wants to have to learn a ton of theory against an opening that you don't face that often?

The Tromp is just one damned annoying opening! I look at it for White and I see loads of playable Black responses. I turn the board round and as Black I don't feel entirely comfortable with any of them!

What's wrong with 3...ef6? The lines look very good for Black.

I'll back this recommendation : 2. ...d5 and it's up to White to show how dangerous his Bg5 really is. Especially as you are familiar with 1...d5-lines.

I have a lot of experience in the tromp from the white side.
I found most annoying the lines with 2...Ne4 followed by 3...c5, but maybe it is more precise to play 2...c5 firse as this "forces" white to decide what to do with the d pawn immediately, without having the chance to gain a tempo on the Ne4 with f3.
2...e6 may also be critical if white insists in remaining in tromp field if black plays in french style, but in my view 3.Nf3 (leading to a torre) is absolutely ok for white and somewhat odd for black if in need of a win.

I've always played 1...d5 up until now but have started playing 1...Nf6 instead.

However, I have a lot of problems against the Trompowsky. Up until now I've been playing 2...e6 wihtout any further knowledge. The reason is that I've heard it is supposed to be the best defence according to theory and it seems less theory critical than Ne4 business.

Can someone briefly explain the alternatives (like 2...Ne4). How much theory? What is the characther of the middlegame etc.? I know the question is elementary but I'm fairly new to 1.e4 having played it only a few months.

Thanks!
Gerbarts