A class of one-dimensional continuum fluid models is defined in which classical particles interact through translationally invariant, strongly tempered manybody potentials meeting conditions sufficient to ensure a proper thermodynamic limit. However, an exact analysis demonstrates that for certain ranges of parameter values the pressure versus density isotherms are discontinuous. The basic models also entail discontinuous temperature versus configurational entropy isobars but extended models are described which exhibit either type of anomaly alone and various unobserved but thermodynamically allowed, anomalous types of first-order transitions.