The linear stability theory (LST) was used to study the confluent shear layer/boundary layer flows. The mean velocity profile exhibited a superposition of the Blasius boundary layer and a shear layer expressed as hyperbolic tangent function. A global method with high order difference schemes was used to solve the Orr-Sommerfeld equation. The numerical procedure was validated by comparing the present results for boundary layer and shear layer with the published articles. The unstable wave modes associated with both shear layer and boundary layer were identified. On this basis

the interactions between the boundary layer mode and the shear layer were examined. Due to the presence of the shear layer

the neutral curve of the boundary layer mode moved to the upper left

resulting in decrease of critical Reynolds number. When the shear layer was brought close to the wall

the boundary layer unstable mode may be destabilized or stabilized

depending upon the disturbance frequency. In the confluent flow

the wall boundary layer has a stabilized effect on the shear layer mode

which occurs in the low frequency range.