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We investigated if greenness and air pollution exposure in parents' childhood affect offspring asthma and hay fever, and if effects were mediated through parental asthma, pregnancy greenness/pollution exposure, and offspring exposure. We analysed 1106 parents with 1949 offspring (mean age 35 and 6) from the Respiratory Health in Northern Europe, Spain and Australia (RHINESSA) generation study. Mean particulate matter (PM_2.5 and PM₁₀), nitrogen dioxide (NO₂), black carbon (BC), ozone (O₃) (µg/m³) and greenness (normalized difference vegetation index (NDVI)) were calculated for parents 0-18 years old and offspring 0-10 years old, and were categorised in tertiles. We performed logistic regression and mediation analyses for two-pollutant models (clustered by family and centre, stratified by parental lines, and adjusted for grandparental asthma and education). Maternal medium PM_2.5 and PM₁₀ exposure was associated with higher offspring asthma risk (odds ratio (OR) 2.23, 95%CI 1.32-3.78, OR 2.27, 95%CI 1.36-3.80), and paternal high BC exposure with lower asthma risk (OR 0.31, 95%CI 0.11-0.87). Hay fever risk increased for offspring of fathers with medium O₃ exposure (OR 4.15, 95%CI 1.28-13.50) and mothers with high PM₁₀ exposure (OR 2.66, 95%CI 1.19-5.91). The effect of maternal PM₁₀ exposure on offspring asthma was direct, while for hay fever, it was mediated through exposures in pregnancy and offspring's own exposures. Paternal O₃ exposure had a direct effect on offspring hay fever. To conclude, parental exposure to air pollution appears to influence the risk of asthma and allergies in future offspring.