The article investigates incomes and especially state pensions 2008 among elderly immigrants who arrived in Sweden before 1970. At age 70 and above, the level of state old‐age pension for immigrant men was nearly the same and for immigrant women somewhat higher than for natives with similar characteristics. At age 65–66 the state pension was lower for immigrants than for their native counterparts. The differences in pensions for immigrants of different ages are probably due to changed rules in the Swedish state old‐age pension system from 2003. The new rules have hit different age groups in different ways. The gaps are partially levelled out when other incomes are included. The extent to which levelling occurs varies greatly between different immigrant groups. For immigrants who have arrived during the last decades, the future state old‐age pension outcomes are expected to be worse. Policy Implications The Swedish Pensions Agency should set up a register of pensions from abroad. This will tell us to what extent old‐age pensions from the home country compensate for low old‐age pensions from the Swedish system. Better integration on the labour market is a powerful measure for reducing the risk of future low pensions among immigrants. This is a challenge for Swedish integration policy. To what extent can other parts of the Swedish welfare system in the future compensate individuals with low old‐age pensions?