The size distributions of nanoparticles in flames are measured using a novel particle mass spectrometer (PMS), which is developed for the size range between 0.3 and 50 nm and for number concentrations between 10(9) and 10(13). Using this instrument the particles are sampled without prior dilution from the flame into a molecular beam. The charged nanoparticles are then deflected by an electric field, to determine the mass according to the time-of-flight principle. The PMS is installed in a low pressure combustion chamber operated at 30 mbar. Measurements are made on primary soot particles and iron oxide particles in a laminar, premixed acetylene/oxygen flame. The soot particles increase in size as a function of the height above the burner and the C/O ratio from 2 up to 10 nm. Iron oxide particles of 3-5 nm are detected as a function of burner height. The soot particles form more rapidly than the iron oxide particles. A model calculation for the formation of silica and iron oxide in hydrogen/oxygen flames is developed, based on previously published reaction mechanisms. On adding a mono-disperse particle coagulation scheme, the time history of the particle number concentration and the particle size is calculated. In agreement with experimental data, the calculations show that iron oxide particles are formed more slowly than silica particles.