Let   be the empirical process corresponding to n i.i.d. random vectores with distribution function F = F₀on R_k. We consider ”Cramr-von Misesstatistics“   with K a cibtinuous function on R, and P_n a probability measure which is allowed to depend on the value of the random vectores. We prove weak convergence of   F = F₀ as well as for sequences F = F_n converging to F₀ in an appropriate manner. Analogue results are derived for some empirical “independenceprocess“  . Our considerations are based on the theory of weak convergence of measures on metric spaces.