[en] With the crystal spectrometer at Muon Channel I at SIN we measured the 3dsub(5/2)-2psub(3/2) X-ray transitions in muonic ²⁵Mg and ²⁷Al. The h.f.s. of the 2psub(3/2) was resoloved and the spectroscopic quadrupole moment of the nuclear ground states determined: Q(²⁵Mg) = +0.201 +- 0.003 b, Q(²⁷Al) = +0.150 +- 0.006 b. We find agreement between the intrinsic quadrupole moment value derived form Q(²⁵Mg) with those calculated from measured B(E2) values. This indicates that for ²⁵Mg the strong-coupling limit of the rotational model with an axially symmetric charge distribution is realized in the lower part of the ground-state rotational band. We combine the quadrupole moments Q with the quadrupole coupling constants measured in electronic atoms of ²⁵Mg and ²⁷Al and derive the electric field gradients as the nucleus (in units of e x a^-3sub(o), where asub(o) is the Bohr radius): [sup(dE)/sub(dz)] = 0.339 +- 0.005 for the ³P₂ state of ²⁵Mg, [sup(dE)/sub(dz)] = 0.54 +- 0.02 for the ²Psub(3/2) state of ²⁷Al. From Hartree-Fock calculations of the ²Psub(3/2) state of Al we derive values for the Sternheimer correction factor R and compare them with calculated values. (orig.)