The paper is devoted to investigation of some properties of [L]-homotopy groups. It is proved, in particular, that for any finite CW -complex L, satisfying double inequality [S] < [L] ≤ [S], π [L] n (S) = Z. Here [L] denotes extension type of complex L and π [L] n (X) denotes n-th [L]-homotopy group of X .