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 mK@. 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.
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