We study the existence and multiplicity of positive solutions for a class of n th-order singular nonlocal boundary value problems u ( n ) ( t ) + a ( t ) f ( t , u ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = 0 , u ' ( 0 ) = 0 , … , u ( n − 2 ) ( 0 ) = 0 , α u ( η ) = u ( 1 ) , where 0 < η < 1 ,     0 < α η n − 1   < 1 . The singularity may appear at t = 0 and/or t = 1 . The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.