  Necessary optimality conditions in the form of the maximum principle for
control problems with infinite time horizon are considered. Both finite and
infinite values of objective functional are allowed since the concept of
overtaking or weakly overtaking optimality is used. New form of optimality
condition is obtained and compared with the transversality conditions usually
used in the literature. The examples, where these transversality conditions may
fail while the new condition holds are presented. For Ramsey problem of capital
accumulation a simple form of necessary optimality conditions is derived, which
is also valid in the case of zero discounting.
