1. **Problem Statement:** Given two parallel lines AB and CD, with angles \(\angle BNO = 128^\circ\) and \(\angle COM = 56^\circ\), find \(\angle MON\) and \(\angle DON\).\n\n2. **Key Information and Rules:**\n- Since AB \(\parallel\) CD, alternate interior angles and corresponding angles formed by transversals are equal.\n- The points O, M, N lie such that OM and ON are transversals intersecting the parallel lines.\n- \(\angle BNO = 128^\circ\) is an exterior angle at point N on line AB.\n- \(\angle COM = 56^\circ\) is an angle at point O on line CD.\n\n3. **Find \(\angle MON\):**\n- \(\angle BNO = 128^\circ\) and \(\angle MON\) are supplementary because they form a linear pair at point N on line AB.\n- Therefore, \(\angle MON = 180^\circ - 128^\circ = 52^\circ\).\n\n4. **Find \(\angle DON\):**\n- Since AB \(\parallel\) CD and OM, ON are transversals, \(\angle COM = 56^\circ\) and \(\angle DON\) are alternate interior angles.\n- Hence, \(\angle DON = 56^\circ\).\n\n**Final answers:**\n\[\angle MON = 52^\circ, \quad \angle DON = 56^\circ\]