We report on the calculation of the cross sections for the production of positive-charge-conjugation states such as π0, η, e+e-, μ+μ-, and π+π- by a two-photon mechanism in e-e+ and e-e- collisions. We give the precise relationship of the process e+e-->e+e+X (X is any C=+ state) to the corresponding two-photon annihilation process γ+γ-->X, as well as a careful derivation of the equivalent-photon approximation. In the case of the π0 production, we have found that, for the beam energy E in the 1-3 GeV range, the exact total cross section is 20-30% larger than the one calculated previously in the equivalent-photon approximation. However, the introduction of form factors cuts down the exact total cross section, reducing it to within 10% of the equivalent-photon-approximation result. For η production the agreement is even better. Thus it appears that the use of the equivalent-photon approximation is justified in most cases. We discuss detailed angular distributions in this approximation for the case of π+π- production. One important problem which cannot be adequately studied in the equivalent-photon approximation is the degree of noncoplanarity of the π+π- (and the μ+μ-) pair. We have studied this problem using the exact formula and found that, for E=1 GeV, typically 40-50% of pion pairs will be produced with the noncoplanarity angle greater than 12°. We discuss the general structure of the γ+γ-->π++π- amplitude as well as a simple model incorporating the σ meson. We also give a rough estimate of multihadron production cross sections.