[en] Complete text of publication follows. There has been much interest recently in phase transitions in various nuclear systems. The phases are defined as (local) minima of the potential energy surface (PES) defined in terms of parameters characterizing the nuclear system. Phase transitions occur when some relevant parameter is changed gradually and the system moves from one phase to another one. In the analysis of such systems the key questions are the number of phases and the order of phase transition between them. Algebraic nuclear structure models are especially interesting from the phase transition point of view, because the different phases may be characterized by different symmetries of the system. Much work has been done recently on models based on the interacting boson approximation (IBA). In these studies the potential energy surface is constructed from the algebraic Hamiltonian by its geometric mapping using the coherent state formalism. Inspired by these studies we performed a similar analysis of a family of algebraic cluster models based on the semimicroscopic algebraic cluster model (SACM). This model has two dynamical symmetries: the SU(3) and SO(4) limits are believed to correspond to vibration around a spherical equilibrium shape and static dipole deformation, respectively. The semimicroscopic nature of this model is reflected by the fact that a fully antisymmetrized microscopic model space is combined with a phenomenologic Hamiltonian that describes excitations of the (typically) two-cluster system. The microscopic model space is necessary to take into account the Pauli exclusion principle acting between the nucleons of the closely interacting clusters. In practice this means that the number of excitation quanta in the relative motion of the clusters has to exceed a certain number n₀ characterizing the system. This is clearly a novelty with respect to other algebraic models, and it complicates the formalism considerably. We thus introduced as a special limit the phenomenologic algebraic cluster model (PACM), in which the n₀ = 0 choice was made. With this choice we ignore a fundamental principle, but in exchange the formalism becomes similar to that of other algebraic models. Our aim was also to explore the consequences of this approximation. In the first step we constructed the PES of the SACM using coherent states. For this we also modified the formalism of the SACM to the present analysis. This included incorporating a third-order term in the Hamiltonian that stabilizes the spectrum for large values of intercluster excitation quanta (π bosons). The parametrization of the Hamiltonian was also changed to allow for a transition between the SU(3) to the SO(4) limits. The results indicated that the effects of the Pauli principle can be simulated in the PACM by incorporating higher-order terms on the Hamiltonian. In the second step we turned to the analysis of phase transitions both in the SACM and the PACM. The potential energy surface typically contained up to two minima, one spherical and one deformed. The analysis identified both first- and second-order phase transitions for the PACM and the SACM, while in the latter case a critical line was also found. The results were illustrated with numerical studies on the ¹⁶O+α and ²⁰Ne+α systems, which correspond to two spherical clusters and to one spherical and one deformed cluster, respectively. The SU(3) limit was found to be the most appropriate one in reproducing the data of the cluster systems. Clear phase transitions were identified in the parameter controlling the transition between the SU(3) and SO(4) limits. It was found that the PACM led to energy spectra that are rather different from the observed physical ones.