We present results for the strong widths corresponding to the Sigma(c)->Lambda(c)pi, Sigma(c)(*)->Lambda(c)pi and Xi(c)(*)->Xi(c)pi decays. The calculations have been done in a nonrelativistic constituent quark model with wave functions that take advantage of the constraints imposed by heavy quark symmetry. Partial conservation of axial current hypothesis allows us to determine the strong vertices from an analysis of the axial current matrix elements. Our results Gamma(Sigma(c)(++)->Lambda(c)(+)pi(+))=2.41 +/- 0.07 +/- 0.02 MeV, Gamma(Sigma(c)(+)->Lambda(c)(+)pi(0))=2.79 +/- 0.08 +/- 0.02 MeV, Gamma(Sigma(c)(0)->Lambda(c)(+)pi(-))=2.37 +/- 0.07 +/- 0.02 MeV, Gamma(Sigma(c)(*++)->Lambda(c)(+)pi(+))=17.52 +/- 0.74 +/- 0.12 MeV, Gamma(Sigma(c)(*+)->Lambda(c)(+)pi(0))=17.31 +/- 0.73 +/- 0.12 MeV, Gamma(Sigma(c)(*0)->Lambda(c)(+)pi(-))=16.90 +/- 0.71 +/- 0.12 MeV, Gamma(Xi(c)(*+)->Xi(c)(0)pi(+)+Xi(c)(+)pi(0))=3.18 +/- 0.10 +/- 0.01 MeV, and Gamma(Xi(c)(*0)->Xi(c)(+)pi(-)+Xi(c)(0)pi(0))=3.03 +/- 0.10 +/- 0.01 MeV are in good agreement with experimental determinations.