We have investigated magnetic properties of the FeAl${}_{2}$ and Fe${}_{2}$Al${}_{5}$ intermetallic compounds. By measuring the zero-field-cooled and field-cooled static (dc) magnetic susceptibilities in low and high magnetic fields, the frequency-dependent (ac) susceptibility, the magnetization versus the magnetic field, and the thermoremanent magnetization time decay, we found that the magnetic structures of FeAl${}_{2}$ and Fe${}_{2}$Al${}_{5}$ are richer than those published so far in the literature. FeAl${}_{2}$ undergoes complex two-step magnetic ordering. At $T$ \ensuremath{\approx} 32 K, a magnetic phase transition (not yet specified) takes place in which a small fraction of the Fe spins participate, whereas at ${T}_{\mathrm{f}2}$ \ensuremath{\approx} 12 K, the majority spin fraction undergoes a spin-freezing transition to a spin glass phase. Fe${}_{2}$Al${}_{5}$ undergoes a transition to a spin glass phase at the spin freezing temperature ${T}_{\mathrm{f}}$ \ensuremath{\approx} 3 K, which was not reported previously. The spin glass phase in Fe${}_{2}$Al${}_{5}$ is ``soft'' and fragile with respect to the external magnetic field and can only be observed in low magnetic fields below \ensuremath{\sim}100 Oe. The origins of the spin glass ordering in the FeAl${}_{2}$ and Fe${}_{2}$Al${}_{5}$ phases are randomness and frustration that are present on the Fe sublattices of both compounds. In FeAl${}_{2}$, the Fe spins are positioned randomly on the three mixed-occupation Al/Fe sites of the unit cell, whereas in Fe${}_{2}$Al${}_{5}$, partial occupation of the Fe-neighboring Al2 and Al3 atomic sites imposes different degrees of Fe moment screening by the electron cloud, resulting in a random distribution of the magnetic moment sizes. Geometric frustration because of positioning of the antiferromagnetically coupled Fe spins on triangles is present in both compounds as well.