[Alexander]

here is the fragment of the molecule:

-CH₂-CH₂-NH-CO-

on the predicted spectra (MestReNova) I have two neighboring triplets for the CH₂ protons given in bold.

Is that really possible that ordinary triplet (that was expected) is separated into two triplets by imine proton?

[Dan]

Yeah I've seen it before with acetamido substituents. In a non-protic solvent like chloroform (where NH exchange is slow on the timescale of nmr, amides are only about as acidic as alcohols) you can get coupling, which in this case would give you a double triplet. In a protic solvent (like D₂O) you would not see it as proton exchange with the solvent would be rapid.

[Smrt guy]

In my experience heteroatom protons tend not to couple, but I have seen it as well.  So, I would say that it is definitely possible but rare enough that when I see it it comes as a surprise.