In this paper, we report on measurements of the specific heat C of single-crystalline EuxSrl_xTe at temperatures between 60 mK and 15 K and in magnetic fields up to 6 T. Pure antiferromagnetic EuTe shows unusual critical behavior in the vicinity of the N6el temperature T N = 9.8 K with a positive critical exponent instead of the 3d-Heisenberg exponent c~---0.12. Possible reasons for this discrepancy between theory and experiment include magnetic anisotropy effects due to magnetic dipole-dipole interactions, which may give rise to a cross-over of the critical behavior very close to T N. This anisotropy is also seen in the specific heat below 1 K where an exponential decay of C is observed, and in the dependence of the magnetic susceptibility on the direction of the applied field. With increasing dilution of EuTe with nonmagnetic Sr, the critical behavior changes: ~ becomes negative and decreases continuously towards ~ ~-1 at x~x c. This concentration dependence of e was previously observed in the diluted ferromagnetic system EuxSr ~ _xS. Our data thus support that the apparent change in the critical behavior depends on the degree of disorder. Samples with concentration x lower than the critical concentration x c reveal spin-glass behavior in the specific heat. In addition, the dependence of T N on magnetic fields is discussed. The data yield a normalized magnetic phase boundary Bc(T)/Bc(T=O ) vs. TN(B)/TN(B=O ) which is independent of concentration.