Abstract: Almost stochastic dominance has been receiving more attention in the financial and economic literature. In this short note, we characterize the almost first- and second-degree stochastic dominance by requiring one distribution to be ``close to'' a new distribution that dominates or is dominated by another distribution in the traditional sense of the first- and second-order stochastic dominance, respectively. We also investigate the concept of almost stochastic dominance for unbounded random variables.