In this paper we study the boundary behaviour of the family of solutions {uε} to singular perturbation problem Δuε=βε(uε),∣uε∣≤1 in , where a smooth boundary data f is prescribed on the flat portion of . Here is an approximation of identity. If ∇f(z)=0 whenever f(z)=0 then the level sets edaa0dcd88c73235cb6eff248" title="Click to view the MathML source">∂{uε>0} approach the fixed boundary in tangential fashion with uniform speed. The methods we employ here use delicate analysis of local solutions, along with elaborated version of the so-called monotonicity formulas and classification of global profiles.