Cdk5/p25 is a member of the family of cyclin-dependent, Ser/Thr kinases and is thought to play a causal role in Alzheimer's disease (AD) due to its ability to phosphorylate the protein tau, and thus promote the latter's aggregation into intraneuronal tangles. Given this, we and others are seeking inhibitors of cdk5/p25 as possible disease-modifying therapeutics for AD. In this paper, we first report the kinetic mechanism for the cdk5/p25-catalyzed phosphorylation of tau and histone H-1-derived peptide (H1P). These studies served as a necessary kinetic backdrop for investigations of the mechanism of inhibition by prototype inhibitors N4-(6-aminopyrimidin-4-yl)-sulfanilamide (APS) and 1-(5-cyclobutyl-thiazol-2-yl)-3-isoquinolin-5-yl-urea (CTIU). We found that the cdk5/p25-catalyzed phosphorylation of tau follows a rapid equilibrium, random kinetic mechanism, as evidenced by initial velocity analysis indicating sequential addition of tau and ATP, and studies of the mechanism of inhibition by substrate analogue AMP, product ADP, and analogues of peptide substrate H1P. Identical mechanistic conclusions were drawn when H1P was the phosphoryl acceptor. Subsequent studies of inhibition by APS and CTIU revealed that both compounds can bind to all four steady-state forms of the enzyme, to form the complexes E:I, E:I:tau, E:I:ATP, and E:I:tau:ATP. These results contrast with reported claims that APS and CTIU are competitive inhibitors of the binding of ATP.