We applied magnetic force microscopy to study the domain structure of Co/Pt multilayers [15 x Co(3.5 Angstrom)/Pt (6 Angstrom)]. The Co/Pt multilayers were deposited on glass substrates and demagnetized either by lowering the external field or by using an oscillating field. We found that both techniques used to demagnetize our samples led to different domain structure. In the first case, domains had different widths in the range from 0.5 to 5 mu m. The other technique (an oscillating field) led to domains more uniform in size with a much smaller width of 70-130 nm. We also studied the stability of the domain structure of Co/Pt multilayers while an external field was applied.