We present some key probability inequalities and convergence results for multisample, or ‘generalized’ U-statistics. The reverse martingale structure of generalized U-statistic is exploited to obtain a useful Kolmogorov-type inequality. In addition, a bound is obtained for the rate of convergence in the strong law of large numbers for generalized U-statistics, expanding the one-sample result of Grams and Serfling (1973). Also, using a forward martingale representation, an invariance principle for generalized U-statistics is established.