This paper proposes new tests of randomness for innovations of a large class of time series models. These tests are based on functionals of empirical processes constructed either from the model residuals or from their associated ranks. The asymptotic behavior of these empirical processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors when appropriate regularity conditions hold. Several test statistics are derived from these processes; the classical BDS statistic and a rank-based analogue thereof are included as special cases. Since the limiting distributions of the rank-based test statistics are margin-free, their finite-sample P-values can easily be calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several alternatives.