We analyse the problem of intracavity second harmonic generation to determine properties of the antiphased states that have been observed in this system. We study the time-periodic solutions by means of a perturbation expansion in powers of a small parameter which is the ratio of the cavity lifetime to the population inversion relaxation time. We prove that each mode intensity is characterized by two oscillation frequencies though the total intensity oscillates with only one of these frequencies. In first approximation, we find that the bifurcation from the steady state to the periodic state remains vertical. We resolve this singularity by a complementary numerical analysis. We show that there are at least four distinct types of antiphase dynamics, including partial clustering of the oscillating modes into subsets of antiphasing states. Finally, we analyse the scaling exponent of the oscillation amplitudes near the bifurcation point and determine that the generic 1/2 exponent is the rule for only two of four types of antiphasing. The exponents of the other two cases depend on the mode number and partition.