Their own statement of belief:
The teaching of the Church of the East is based on the faith of the universal Church as set forth in the Nicene Creed. The mystery of the Holy Trinity and the mystery of the Incarnation are central to its teaching. The church believes in One Triune God: Father, Son, and Holy Spirit. It also believes and teaches that the Only-begotten Son of God, God the Word, became incarnate for us men and for our salvation and became man. The same God the Word, begotten of his Father before all worlds without beginning according to his divinity, was begotten of a mother without a father in the last times according to his humanity, in a body of flesh, with a rational, intelligent, and immortal soul which he took from the womb of the Blessed Virgin Mary and united to himself, making it his very own at the moment of conception. The humanity which he took for his own was assumed by God the Word, who was, thenceforth and for ever, the personal subject of the divine and human natures. His divine and human natures retain their own properties, faculties, and operations unconfusedly, immutably, undividedly, and inseparably.
Therefore, because the divinity and humanity are united in the Person of the same and only Son of God and Lord Jesus Christ, the Church of the East rejects any teaching which suggests that Christ is an "ordinary man" whom God the Word inhabited, like the righteous men and the prophets of old. The Church of the East further rejects any teaching that explicitly or implicitly suggests that there are two Sons, or two Lords, or two Christs in our Lord and Savior Jesus Christ, but we confess one Lord Jesus Christ, the Son of God, who is the same yesterday, today, and forever. The same, through his passion, death, burial, and resurrection, redeemed humanity from the bondage of sin and death, and secured the hope of resurrection and new life for all who put their faith in him, to whom, with his Father and the Holy Spirit, belongs confession, worship, and adoration unto ages of ages. Amen.
If this is the Assyrian Church's belief statement, then they would not be Nestorian.
This is from Wikipedia:
"Although the Assyrian Church split from the western churches in the course of the Nestorian schism, the theology of the Assyrian church can not be defined as Nestorianism. Nestorius, a pupil of Theodore of Mopsuestia and bishop of Constantinople, was condemned because he refused to call the Virgin Mary 'mother of God'. He would only call her 'mother of Christ'. His opponent Cyril of Alexandria accused him of dividing Christ into two persons, which he clearly denied. The affair was complicated by the unclear arguments of Cyril, which soon after provoked the Monophysite schism."http://en.wikipedia.org/wiki/Assyrian_Church_of_the_East
May peace be upon thee and with thy spirit.