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We present a radiative equilibrium model for extrasolar giant planets applied to 51 Peg b. The atmospheric model extends from [10.sup.-5] to ~ 10 bar and is limited at the bottom by an optically thick cloud of silicate ([Mg.sub.2]Si[O.sub.4] or MgSi[O.sub.3]) or iron (Fe) particles. Rayleigh scattering at short wavelengths and absorption by the [H.sub.2]--[H.sub.2] and [H.sub.2]--He continuum and molecular bands of [H.sub.2]O, CO, and [CH.sub.4] are included. Atmospheric heating and cooling result, respectively, from absorption of stellar flux and from infrared thermal emission. The solution temperature profiles do not show any temperature inversion, in contrast with the giant planets of the solar system. The lapse rate is subadiabatic at all levels above the cloudtop, justifying the use of radiative equilibrium. We find that, under thermochemical equilibrium, CO dominates over [CH.sub.4] at all levels. The effective temperature is in the range 1150-1270 K and the Bond albedo in the range 0.15-0.42, depending on the location and reflectivity of the lower cloud deck. [Mg.sub.2]Si[O.sub.4] or Fe clouds are weakly reflective in contrast to a MgSi[O.sub.3] cloud. The thermal emission spectrum prevails over the stellar reflected component below 13,000--15,000 [cm.sup.-1] ([Lambda] [is greater than] 0.7 [micro]m); it shows various windows, between the [H.sub.2]O and CO bands, with the brightest centered at 2550 [cm.sup.-1] (3.9 [micro]m). The most prominent CO and [CH.sub.4] bands occur around 2100 (4.7 [micro]m) and 3030 [cm.sup.-1] (3.3 [micro]m). Assuming a jovian abundance for [PH.sub.3], the bands around 2300 (4.3 [micro]m) and 2450 [cm.sup.-1] (4.1 [micro]m) are clearly visible in absorption at a resolving power of ~ 100. We investigated the detectability of the minor species CO and [CH.sub.4] at a resolution of 4000--6000, adequate to separate the planet's absorption features from their stellar and telluric counterparts. Considering photon noise from the star as the only noise source, we find that S/N ratios of about 8 are reached on the molecular features in the 4.7- and 3.3-[micro]m regions after ~ 10 h of integration on an 8-m telescope. On the other hand, the planet-to-star contrast is as low as (2-4) x [10.sup.-4]. Key Words: atmosphere, structure; atmosphere, composition; extrasolar planets.