Fixed point theorems are established under three types of general contraction conditions in a G-metric space (X, G): one is of Nesic-type and two of twice-power contraction type. Further, the fixed point p obtained for a twice-power contraction f will be a G-contractive fixed point, in the sense that for each x∈ X, the f-iterates x, fx, f2x, … converge to p in X. © 2017, Forum D'Analystes, Chennai.