  The intermediate-valent polymorphs $\alpha$- and $\beta$-YbAlB$_4$ exhibit
quantum criticality and other novel properties not usually associated with
intermediate valence. Iron doping induces quantum criticality in
$\alpha$-YbAlB$_4$ and magnetic order in both compounds. We report results of
muon spin relaxation ($\mu$SR) experiments in the intermediate-valent alloys
$\alpha$-YbAl$_{1-x}$Fe$_x$B$_4$, $x = 0.014$ and 0.25. For $x = 0.014$ we find
no evidence for magnetic order down to 25<EMAIL_ADDRESS>The dynamic muon spin
relaxation rate $\lambda_d$ exhibits a power-law temperature dependence
$\lambda_d \propto T^{-a}$, $a = 0.40(4)$, in the temperature range 100 mK--2
K, in disagreement with predictions by theories of antiferromagnetic (AFM) or
valence quantum critical behavior. For $x = 0.25$, where AFM order develops in
the temperature range 7.5--10 K, where we find coexistence of meso- or
macroscopically segregated paramagnetic and AFM phases, with considerable
disorder in the latter down to 2 K.
