  Precise measurements of the thermodynamic critical field ($B_{\rm c}$) in
type-I noncentrosymmetric superconductor BeAu were performed by means of the
muon-spin rotation/relaxation technique. The temperature evolution of $B_{\rm
c}$ can not be described within the single gap scenario and it requires the
presence of at least two different types of the superconducting order
parameters. The self-consistent two-gap approach, adapted for analysis of
$B_{\rm c}(T)$ behavior, suggests the presence of two superconducing energy
gaps with the gap to $T_{\rm c}$ ratios $2\Delta/k_{\rm B}T_{\rm c}\simeq4.52$
and $\simeq2.37$ for the big and the small gap, respectively. This implies that
the superconductivity in BeAu is unconventional and that the supercarrier
pairing occurs at various energy bands.
