Thisi is of a vital importance for me, I need to know if the MOXF is capable of a Non-Stop Recording method to record a synth or bass or drum part during a live performance, without stopping the workflow recording process for every new part.
If I understand right, also by watching a MOXF demo video on youtube and by reading the manual, it seems that after recording a new part, it will not be playback immediately in a REC--->PLAY way, but after I've recorded a new part I have to press first the Stop button and then the Play button or TOP and then Play button to hear my newly recorded performance.

This is not a nice behaviour for me, during a live performance, could someone help me to understand how could I set the MOXF for a Non-Stop Recording method?

PATTERN Mode. The explanation is that simple.

If you record in the linear Song mode, yes your workflow would include stopping and rewinding. This is the long standing workflow for music recording. But this is certainly not the only workflow available to composers with the MOXF. Not sure of which particular video you were watching but it certainly was not one that deals with what you want to accomplish - it probably was demonstrating a more "normal" (typical) method of recording. For what you want to accomplish you want to look to recording in PATTERN mode. Pattern mode allows you realtime access and recording in cycling/looping Sections. The fact that recording can be done by creating looping phrases opens the door to the type workflow you are describing.

Yamaha's Music Production synthesizers have PATTERN mode where recording can be done without ever hitting the STOP button (if you don't want to). You can drop in and out of record without hitting stop, you can select sounds for the different PARTS and move from track to track when you need to... there are the following things you need to know. You must set a LENGTH... this can be from 001 to 256 Measures... the reason is that Pattern mode will cycle and you must define the Time Signature, Tempo and Length before you begin. Recording on a selected track requires you respect your LENGTH setting. By this I mean - say you setup a 16 measure Length - as you record on Track 1 your recording will continue from measure 001 to the end of measure 016, and then cycle. To move the RECORD function to another track, simply press the Track's number button. Recording on that track will begin when the Pattern cycles back to measure 001. This does not present a major problem as you must record your phrases for each track while the RED Record light is lit and you pass GO (GO in this case is the marker at measure 001, beat 1, clock 000).

You can easily record a Track, drop out of record, select a new Track, assign an instrument, drop back into record, lay down the new data, and so on, all without ever hitting stop.
What most people do in a live record situation is prepare the Instruments they are going to use ahead of time - MIXING Templates can be stored in memory for recall. Moving between tracks is seamless and easy to do.

And since you can quantize as you record, and/or after the fact; destructively or non-destructively - there is no reason to press STOP until you finished with this particular session. Whether or not this will fit your exact needs is really only for you to say - Obviously, every person's workflow can be different. So only you can determine if you can work within any given system.

We also highly recommend you make your decision based on more than just this requirement - but rest assured you can record an entire PATTERN sequence (all 16 tracks) without hitting stop if you don't wish to.

We should also mention that while the Pattern sequencer is loop recording, you have access to over 7,900 arpeggio phrases. These phases can be recalled and fully controlled in real time. You can drop beats in, in realtime, interact with them, use the real time Play FX to alter feel and attitude of the phrases. They are additional chord intelligent, where appropriate, so they can instantly accommodate your musical needs. Four independent Arpeggiators are available and all feature real time access.

In fact, the arpeggiators offer an alternate method as they provide a real time access function you may find compelling. Not only are their the more than 7900 phrases you can prepare your own custom data for use as arpeggio phrases.