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The protons which repeal each other electrostatically & the neutron which exert no electric force are held extremely close together inside a stable nucleus.
Obviously there are some forces operating within the nucleus which binds neutron to proton (n-p forces), proton to protons ( p-p forces) and neutron to neutron (n-n forces). These forces bind the nucleus.
Nuclear forces has following properties :
i) They are attractive : The overall effect of Nuclear forces is attractive otherwise the nucleus will not exist. 
ii) They are non electric : The nuclear forces cannot be of electrical nature. If it will so, the protons will repel one another. 
iii) They are non gravitational. 

iv) They are extremely strong : The nuclear forces are strongest known forces in nature. Therefore they provide stability to nucleus. 
v) They are extremely short range forces : These forces are applicable only in a small region of order of 10^-15 m. These forces donot obey inverse square law. 
vi) They are spin dependent :  Experimental evidences shows that the nuclear force acting between two nucleons depends upon the mutual orientation of spins of nucleons. e.g. a neutron and a proton are kept together forming a deutron only if their spins are parallel to each other.