At first the author proves a generalization of coincidence theorem due to Walsh, improving some results of A. Aziz. As a consequence the following theorem is verified. Suppose that \( p(z) \) is a complex polynomial of degree \( n \) whose \( (n-1) \) zeroes are contained in the closes disk \( D \). The centre of \( D \) is the arithmetic mean of these zeroes. Then \( D \) contains at least \( [ \frac{n-2k+1}{2}] \) zeroes of \( p^{(k)}(z) \). A variation of Szegö composition theorem is proved too.