The concept of congruence kernels and congruence cokernels are studied in pseudocomplemented almost distributive lattices. A set of equivalent conditions are derived for a given subset J of a pseudocomplemented ADL L to be a congruence kernel (resp. a congruence cokernel). Moreover, for a given congruence kernel J of L the smallest and the largest *- congruences on L having J as a kernel are given and characterized in various forms.