In rapidly solidified $Al_{92-x}Nd_8$(Cu,Ag)x ($0{leq}X{leq}10at%$) alloys, amorphous single phases were obtained in the ranges of $Oat%{leq}X{leq}4at%$ for Al-Nd-Cu system and $Oat%{leq}X{leq}6at%$ for Al-Nd-Ag system, respectively. Mesoscopic structures consisted of amorphous and crystalline phases were formed above solute ranges. It was founded that the mesoscopic structures were also formed near 1st exothermic peak on DSC curve by aging in amorphous single phase alloys. For example, amorphous $Al_{92-x}Nd_8$(Cu,Ag)x (X=2.4at%) alloys containing nanoscale Al particles and compounds, i.e., mesoscopic structure, exhibited higher tensile fracture strength(${sigma}_f$) than those of amorphous single phase alloys with the same composition. The ${sigma}_f$ showed a maximum value in the $V_f$ ranges of 10~15%. The reason is presumed that the nanoscale precipitates which have higher mechanical strength compared with the amorphous phase with the same composition act as an effective resistance to shear deformation of the amorphous matrix.