Consider a graph G = (V, E) and a random initial vertex-coloring, where each vertex is blue independently with probability p b , and red with probability p r = 1 − p b . In each step, all vertices change their current color synchronously to the most frequent color in their neighborhood and in case of a tie, a vertex conserves its current color; this model is called majority model. If in case of a tie a vertex always chooses blue color, it is called biased majority model. We are interested in the behavior of these deterministic processes, especially in a two-dimensional torus (i.e., cellular automaton with (biased) majority rule). In the present paper, as a main result we prove both majority and biased majority cellular automata exhibit a threshold behavior with two phase transitions. More precisely, it is shown that for a two-dimensional torus T n,n , there are two thresholds 0 ≤ p 1 , p 2 ≤ 1 such that p b p 1 , p 1 p b p 2 , and p 2 p b result in monochromatic configuration by red, stable coexistence of both colors, and monochromatic configuration by blue, respectively in O(n 2 ) number of steps.