The potential energy curves have been investigated for the 15 lowest doublet and quartet electronic states in the (2s+1)A(+/-) representation of the molecule NaYb via CASSCF/MRCI (single and double excitations with Davidson correction) calculations. The spectroscopic constants (T-e, D-e, omega(e), B-e, r(e),...) have been calculated in addition to the permanent dipole moments A. By using the canonical functions approach, the eigenvalues E-v, the rotational constants B-v, the centrifugal distortion constant D-v, and the abscissas of the turning points r(min) and r(max) have been calculated for different electronic states. Fourteen molecular states have been studied theoretically for the first time. (C) 2015 Elsevier B.V. All rights reserved.