In this paper on topological spaces we formulate new monotone principles of fixed point, forked point and fixed apex. This text continues the further study of the paper by M. R. Tasković [A monotone principle of fixed points, Proc. Amer. Math. Soc., 94 (1985), 427-432, Lemma 2 and Theorem 2]. New monotone principles to include some recent results of author, which contains, as special cases, some results of S. Banach, J. Dugundji and A. Granas, F. Browder, D. W. Boyd and J. S. Wong, J. Caristi, T. L. Hicks and B. E. Rhoades, B. Fisher, S. Massa, Ð. Kurepa, M. Kwapisz, W. Kirk, S. Park, M. Krasnoselskij, V. J. Stečenko, T. Kiventidis, I. Rus, K. Iséki, J. Walter, J. Daneš, A. Meir and E. Keeler, L. Collatz, J. Istrăţescu, A. Miczko, and B. Palczewski, C. S. Wong, and many others.