Abstract: The total and differential cross sections for associated strangeness production in the pp -> pK(+) K(-)p and pp -> pK(+)pi(0)Sigma(0) reactions have been studied in a unified approach using an effective Lagrangian model. It is assumed that both the K(-)p and pi(0)Sigma(0) final states originate from the decay of the Lambda(1405) that was formed in the production chain pp -> p(N*(1535). K+ Lambda(1405)). The available experimental data are well reproduced, especially the ratio of the two total cross sections, which is much less sensitive to the particular model of the entrance channel. The significant coupling of the N*(1535) to Lambda(1405)K is further evidence for large ss components in the quark wave function of the N*(1535).