In　this　paper,　we　study　the　ultraweak-local　discontinuous　Galerkin　(UWLDG)　method　for　time　-dependent　linear　fourth　-order　problems　with　four　types　of　boundary　conditions.　In　one　dimension　and　two　dimensions,　stability　and　optimal　error　estimates　of　order　k　+　1　are　derived　for　the　UWLDG　scheme　with　polynomials　of　degree　at　most　k　(k　＞=　1)　for　solving　initial　-boundary　value　problems.　The　main　difficulties　are　the　design　of　suitable　penalty　terms　at　the　boundary　for　numerical　fluxes　and　the　construction　of　projections.　More　precisely,　in　two　dimensions　with　the　Dirichlet　boundary　condition,　an　elaborate　projection　of　the　exact　boundary　condition　is　proposed　as　the　boundary　flux,　which,　in　combination　with　some　proper　penalty　terms,　leads　to　the　stability　and　optimal　error　estimates.　For　other　three　types　of　boundary　conditions,　optimal　error　estimates　can　also　be　proved　for　fluxes　without　any　penalty　terms　when　special　projections　are　designed　to　match　different　boundary　conditions.　Numerical　experiments　are　presented　to　confirm　the　sharpness　of　theoretical　results.