The gas to particle conversion process in the atmosphere may either lead to condensation on existing aerosol or the nucleation of fresh aerosol. Bursts of nucleation corresponding to the production of sulphuric acid aerosol, and possibly also of ammonium sulphate aerosol, have been observed to take place. The corresponding increase in atmospheric aerosol leads to increased reflection of solar radiation and an increase in the concentration of cloud condensation nuclei, both of which have a net cooling effect on the climate. The nucleation processes need to be specified analytically if possible, because their timescales may be shorter than other aerosol processes so that they would take place on a sub-grid scale in a large atmospheric model. We have extended the analytic nucleation treatments of Barrett and Clement (1991) and Barrett (1992) in order to obtain analytic results for nucleation timescales and numbers of nuclei produced.We treat two kinds of nucleation, the first being binary homogeneous nucleation of sulphuric acid where the nucleation rate depends on a high power of the sulphuric acid monomer concentration (Easter and Peters 1993). The second type of nucleation is typified by ammonium sulphate where all clusters are stable and may be termed barrierless or source-enhanced nucleation. (Lushkinov and Kulmala 1995) with a production rate 12α 1 c 1 2 in terms of the monomer concentration c 1 . For both types of nucleation we have to solve the equation for the monomer concentration, which, in the barrierless case, takes the following form in terms of c n (t), the concentration of n-mers: where P 1 (t) is the production rate, R A is the removal rate to existing aerosol, and α n is the cluster growth rate by monomer attachment. If the timescale for condensation on existing aerosol, t A = R A - 1 , is shorter than the timescale for the change in P 1 , the initial solution is c 1 = P 1 (t) / R A . As an example of our results, we can then determine the timescale, t c , for removal to the freshly nucleated aerosol to begin to cut off nucleation, which occurs when the final term in eq. becomes equal to P 1 . Assuming molecular sticking probabilities of unity (Clement et al 1996), the result for t A in s and P 1 in cm - 3 s - 1 is Results for removal rates and production rates typical of those in the atmosphere are shown in Table 1. They range from very short times for high production rates in a clean atmosphere (bottom right hand corner of table) to very long times for low production rates in a polluted atmosphere (top left hand corner). Similar calculations have been performed for homogeneous nucleation, where the sensitivity, to t A and P 1 is even greater, and a method has been developed to calculate the numbers of nuclei produced by bursts with a time dependent P 1 (t).