This paper is a systematic study of the critical nature of activities and r
elationships in AON networks with minimal time lags in the unlimited resour
ce case, when activity splitting is not allowed. An analysis of all possibl
e cases produces an extended and now complete classification of critical ac
tivities in six classes: normal, reverse, neutral, bicritical, increasing n
ormal and decreasing reverse. We also present a procedure for classifying a
ny critical task depending on the early star/finish times and on position w
ithin the critical paths.