We show that the OPAL opacities, in addition to explaining the origin of the pulsations of beta Cep stars, also predict the existence of a large region in the main-sequence band at lower luminosities, where high-order g-modes of low harmonic degree l are unstable. The excitation mechanism remains the same, and is due to the usual kappa-effect acting in the metal opacity bump (T almost-equal-to 2 X 10(5) K). The new instability domain nearly bridges the gap in spectral types between delta Sct and beta Cep stars. The periods of the unstable modes are in the range 0.4-3.5 d for l = 1 and 2. We propose that this excitation mechanism causes photometric variability in the slowly pulsating B-type stars (SPB stars), and perhaps in other B stars for which variability in the same period range has been reported. Typically, a large number of modes are simultaneously unstable in one model. Most of them have 1 > 2. Such modes are not likely to be detected photometrically, but may be visible in line profile changes. The excitation of many high-l modes in a star may also cause a spurious contribution to the rotational v sin i values. Sequences of unstable modes at each value of 1 exhibit a periodically varying departure from equal spacing in period. This feature, first noted in white dwarf g-mode spectra (calculated and measured), is in the present case a probe of the region left behind the shrinking core (the mu-gradient zone). We discuss prospects for and difficulties of SPB-star asteroseismology.