I study the egalitarian way of distributing resources across generations. Distributional equity deeply conflicts with the Pareto principle: efficient allocations cannot guarantee that i) each generation be assigned a consumption bundle that is at least as large as an arbitrarily small fraction of the bundle assigned to any other generation and that ii) each generation finds its assigned bundle at least as desirable as an arbitrarily small fraction of the bundle assigned to any other generation with same preferences. Overcoming such tension unveils a new ethical dilemma for intergenerational equity: the short-term/long-term inequality trade-off. The egalitarian ethical observer can choose between: i) "weak equity" among all generations (at the cost of possibly large inequalities among proximate ones) and ii) "strong equity" among few successive generations (at the cost of possibly large inequalities among distant ones). The last alternative is specific to the dynamic framework and provides a rationale to treat generations differently based on their time order.