Let h = u + w, where u,v are real harmonic functions in the unit disc delta. Such functions are called complex mappings harmonic in delta. The function h may be written in the form h = f + g, where f, g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small ([CS-S]) and were continued by many others mathematicians. We can find some papers on functions harmonic in delta, satisfying certain coefficient conditions, e.g. [AZ], [S], [G]. We investigate some more general problems, which appeared during the seminar conducted by Professor Z. Jakubowski.