A B S T R A C TProperties of the so-called strange modes occurring in linear stability calculations of stellar models are discussed. The behaviour of these modes is compared for two different sets of stellar models, for very massive zero-age main-sequence stars and for luminous hydrogendeficient stars, both with high luminosity-to-mass ratios. We have found that the peculiar behaviour of the frequencies of the strange modes with the change of a control parameter is caused by the pulsation amplitude of a particular eigenmode being strongly confined to the outer part of the envelope, around the density inversion zone. The frequency of a strange mode changes because the depth of the confinement zone changes with the control parameter. Weakly non-adiabatic strange modes tend to be overstable because the amplitude confinement quenches the effect of radiative damping. On the other hand, extremely non-adiabatic strange modes become overstable because the perturbation of radiation force (gradient of radiation pressure) provides a restoring force that can be out of phase with the density perturbation. We discuss this mechanism by using a plane-parallel two-zone model.Key words: stars: chemically peculiar -stars: oscillations -stars: variables: other. I N T R O D U C T I O NStrange modes of stellar pulsation were discovered in numerical studies some 20 years ago (Wood 1976). Since then pulsationally unstable strange modes have been found in very different classes of stellar models. Examples are He stars [Saio & Jeffery 1988;Saio, Wheeler & Cox 1984 (in these papers unstable strange modes were identified as ordinary modes); Gautschy & Glatzel 1990;Gautschy 1995;Saio 1995], low-mass supergiants (Aikawa 1985;Worrell 1986;Zalewski 1992;Gautschy 1992a), massive main-sequence stars (Gautschy 1992b;Glatzel & Kiriakidis 1993a;Papaloizou et al. 1997) and evolved massive stars (Glatzel & Kiriakidis 1993b), central stars of planetary nebulae (Gautschy 1993), WR stars (Glatzel, Kiriakidis, Glatzel & Fricke 1996) and classical Cepheids (Buchler, Yecko & Kolláth 1997). It seems likely that the strange mode phenomenon is responsible for the variability of at least some of these stars. Recently, Glatzel (1994), Papaloizou et al. (1997) and Buchler et al. (1997) discussed analytically the origin of the strange modes. Despite the large number of theoretical studies, many of the properties of strange modes have still been puzzling. In this paper we try to clarify some of the properties of strange modes, referring to numerical results for very massive zero-age main-sequence (ZAMS) models and luminous helium stars.The concept of a modal diagram has proved to be a powerful tool in describing the pulsational behaviour of a sequence of stellar models. A linearized stability analysis gives a set of (complex) eigenfrequencies q ¼ ðq R ; q I Þ, called the eigenspectrum S of the model. A series of stellar models is constructed by changing a control parameter, P, such as mass or effective temperature. We shall assume that a continuous change of P lea...

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